\documentclass[12pt,openany,leqno,twocolumn]{book} %Licensed under LaTeX Project Public License 1.3c. %This is a list of definitions for use with the principia package, Version 2.0. %Copyright Landon D. C. Elkind, 2021 (https://landonelkind.com/contact/). \usepackage{newtxtext} %\usepackage{mathptmx} %Principia package requirements \usepackage{pifont} %This loads the eight-pointed asterisk. \usepackage{amssymb} %This loads the relation domain and converse domain limitation symbols. \usepackage{graphicx} %This loads commands that flip iota for definite descriptions, Lambda for the universal class, and so on. The (superseded) graphics package should also work here, but is not recommended. %\usepackage{amssymb} \usepackage{amsmath} %This loads the circumflex, substitution into theorems, \text{}, \mathbf{}, \boldsymbol{}, \overleftarrow{}, \overrightarrow{}, etc. \usepackage{fullpage} \usepackage{perpage} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{mathrsfs} \usepackage[hidelinks,pdfencoding=unicode]{hyperref} \usepackage{enumitem} \usepackage{moreenum} \usepackage[normalem]{ulem} \usepackage[perpage,symbol]{footmisc} \usepackage{setspace} %Volume I %Mathematical logic %The theory of deduction %Meta-logical symbols \newcommand{\ie}{\textit{i}.\textit{e}.\ } \newcommand{\Ie}{\textit{I}.\textit{e}.\ } \newcommand{\eg}{\textit{e}.\textit{g}.\ } \newcommand{\Eg}{\textit{E}.\textit{g}.\ } \newcommand{\pmsch}[1]{\pmast#1} %Starred chapter \newcommand{\pmschs}[2]{\pmast#1\text{---}\pmast#2} %Starred chapter \newcommand{\pmsns}[3]{\pmast#1\pmcdot#2\text{---}\pmcdot#3}%Starred number \newcommand{\pmpsn}[2]{(\pmast#1\pmcdot#2)} \newcommand{\pmpsnn}[3]{(\pmast#1\pmcdot#2\pmcdot#3)} \newcommand{\pmsn}[2]{\pmast#1\pmcdot#2} \newcommand{\pmnsn}[1]{\text{#1}} \newcommand{\pmsnn}[3]{\pmast#1\pmcdot#2\pmcdot#3} \newcommand{\pmsnnn}[4]{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4} \newcommand{\pmsnnnn}[5]{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4\pmcdot#5} \newcommand{\pmsnnnnn}[6]{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4\pmcdot#5\pmcdot#6} \newcommand{\pmsnb}[2]{\boldsymbol{\pmast#1\pmcdot#2}} %Starred number boldface \newcommand{\pmsnnb}[3]{\boldsymbol{\pmast#1\pmcdot#2\pmcdot#3}} \newcommand{\pmsnnnb}[4]{\boldsymbol{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4}} \newcommand{\pmsnnnnb}[5]{\boldsymbol{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4\pmcdot#5}} \newcommand{\pmsnnnnnb}[6]{\boldsymbol{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4\pmcdot#5\pmcdot#6}} \newcommand{\pmfd}{\begin{center} \rule{5cm}{.5pt} \end{center}} %Dividing line between introductory remarks in a starred number and the formal deductions. \newcommand{\pmdem}{\textit{Dem}.} %This notation begins a proof. \newcommand{\pmdemi}{\indent \pmdem} %This idents the notation that begins a proof. \newcommand{\pmhp}{\text{Hp}} %This typesets Hp (short for antecedent), which occurs at the beginning of a proof. \newcommand{\pmprop}{\text{Prop}} %This occurs at the end of a proof. \newcommand{\pmithm}{\pmimp\;\pmthm} %This occurs when a meta-theoretic implication is asserted. \newcommand{\pmbr}[1]{\bigg \lbrack \normalsize #1 \bigg \rbrack} %These are larger brackets for substitution. \newcommand{\pmsub}[2]{\bigg \lbrack \small \begin{array}{c} #1 \\ \hline #2 \end{array} \bigg \rbrack} %This is the substitution command. \newcommand{\pmsubb}[4]{\bigg \lbrack \small \begin{array}{c c} #1, & #3 \\ \hline #2, & #4 \end{array} \bigg \rbrack} %This is the substitution command. \newcommand{\pmsubbb}[6]{\bigg \lbrack \small \begin{array}{c c c} #1, & #3, & #5 \\ \hline #2, & #4, & #6 \end{array} \bigg \rbrack} %This is the substitution command. \newcommand{\pmsubbbb}[8]{\bigg \lbrack \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array} \bigg \rbrack} %This is the substitution command. \newcommand{\pmSub}[3]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array} \bigg \rbrack} %This is the substitution command. \newcommand{\pmSubb}[5]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array} \bigg \rbrack} %This is the substitution command. \newcommand{\pmSubbb}[7]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array} \bigg \rbrack} %This is the substitution command. \newcommand{\pmSubbbb}[9]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c c} #2, & #4, & #6, & #8 \\ \hline #3, & #5, & #7, & #9 \end{array} \bigg \rbrack} %This is the substitution command. \newcommand{\pmsUb}[2]{\small \begin{array}{c} #1 \\ \hline #2 \end{array}} %This is the substitution command. \newcommand{\pmsUbb}[4]{\small \begin{array}{c c} #1, & #3 \\ \hline #2, & #4 \end{array}} %This is the substitution command. \newcommand{\pmsUbbb}[6]{\small \begin{array}{c c c} #1, & #3, & #5 \\ \hline #2, & #4, & #6 \end{array}} %This is the substitution command. \newcommand{\pmsUbbbb}[8]{\small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array}} %This is the substitution command. \newcommand{\pmSUb}[3]{\normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array}} %This is the substitution command. \newcommand{\pmSUbb}[5]{\normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array}} %This is the substitution command. \newcommand{\pmSUbbb}[7]{\normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array}} %This is the substitution command. \newcommand{\pmSUbbbb}[9]{\normalsize #1 \text{ } \small \begin{array}{c c c c} #2, & #4, & #6, & #8 \\ \hline #3, & #5, & #7, & #9 \end{array}} %This is the substitution command. \newcommand{\pmthm}{\mathpunct{\text{\scalebox{.5}[1]{$\boldsymbol\vdash$}}}} %This is the theorem sign. \newcommand{\pmast}{\text{\resizebox{!}{.75\height}{\ding{107}}}} %This is the sign introducing a theorem number. \newcommand{\pmcdot}{\text{\raisebox{.05cm}{$\boldsymbol\cdot$}}} %This is a sign introducing a theorem sub-number. \newcommand{\pmiddf}{\mathbin{=}} \newcommand{\pmdf}{\quad \text{Df}} \newcommand{\pmDf}{\text{Df}} \newcommand{\pmpp}{\quad \text{Pp}} %Square dots for scope, defined for up to six dots \newcommand{\pmd}{\hbox{\rule{.3ex}{.3ex}}} %single square dot \newcommand{\pmdd}{\overset{\pmd}{\pmd}} %vertically aligned pair of square dots \newcommand{\pmdot}{\mathinner{\pmd}} \newcommand{\pmdott}{\mathinner{\pmdd}} \newcommand{\pmdottt}{\mathinner{\pmdd\hspace{1pt}\pmd}} \newcommand{\pmdotttt}{\mathinner{\pmdd\hspace{1pt}\pmdd}} \newcommand{\pmdottttt}{\mathinner{\pmdd\hspace{1pt}\pmdd\hspace{1pt}\pmd}} \newcommand{\pmdotttttt}{\mathinner{\pmdd\hspace{1pt}\pmdd\hspace{1pt}\pmdd}} %Logical connectives \newcommand{\pmnot}{\mathord{\ooalign{$\boldsymbol{\sim}\mkern.5mu$\hidewidth\cr$\boldsymbol{\sim}$\cr\hidewidth$\mkern.5mu\boldsymbol{\sim}$}}} \newcommand{\pmor}{\mathbin{\ooalign{$\boldsymbol{\vee}\mkern.5mu$\hidewidth\cr$\boldsymbol{\vee}$\cr\hidewidth$\mkern.5mu\boldsymbol{\vee}$}}} \newcommand{\pmimp}{\mathbin{\ooalign{$\boldsymbol{\supset}\mkern.5mu$\hidewidth\cr$\boldsymbol{\supset}$\cr\hidewidth$\mkern.5mu\boldsymbol{\supset}$}}} %1.01 \newcommand{\pmand}{\mathbin{\pmd}}%3.01 \newcommand{\pmandd}{\mathbin{\pmdd}} \newcommand{\pmanddd}{\mathbin{\pmdd\hspace{1pt}\pmd}} \newcommand{\pmandddd}{\mathbin{\pmdd\hspace{1pt}\pmdd}} \newcommand{\pmanddddd}{\mathbin{\pmdd\hspace{1pt}\pmdd\hspace{1pt}\pmd}} \newcommand{\pmandddddd}{\mathbin{\pmdd\hspace{1pt}\pmdd\hspace{1pt}\pmdd}} \newcommand{\pmprod}{\mathbin{\ooalign{$\boldsymbol{\wedge}\mkern.5mu$\hidewidth\cr$\boldsymbol{\wedge}$\cr\hidewidth$\mkern.5mu\boldsymbol{\wedge}$}}} %Not in Principia, but added here as a dual of its symbol for disjunction. \newcommand{\pmiff}{\mathbin{\ooalign{$\boldsymbol{\equiv}\mkern.5mu$\hidewidth\cr$\boldsymbol{\equiv}$\cr\hidewidth$\mkern.5mu\boldsymbol{\equiv}$}}} %4.01 \newcommand{\pminc}{\mathbin{|}} %8.01 %The theory of apparent variables \newcommand{\pmall}[1]{(#1)} \newcommand{\pmsome}[1]{(\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}#1)} %10.01 \newcommand{\pmSome}{\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}} %Additional defined logic signs \newcommand{\pmhat}[1]{\hat{#1}} \newcommand{\pmbreve}[1]{\boldsymbol{\breve{#1}}} \newcommand{\pmcirc}[1]{\boldsymbol{\dot{\text{$#1$}}}} \newcommand{\pmpf}[2]{#1#2} %for propositional functions of one variable \newcommand{\pmpff}[3]{#1(#2, #3)} %for propositional functions of two variables \newcommand{\pmpfff}[4]{#1(#2, #3, #4)} %for propositional functions of three variables \newcommand{\pmpffff}[5]{#1(#2, #3, #4, #5)} %for propositional functions of four variables (including ellipses) \newcommand{\pmppf}[2]{#1\pmshr#2} %for propositional predicative functions of one variable \newcommand{\pmppff}[3]{#1\pmshr(#2, #3)} %for propositional predicative functions of two variables \newcommand{\pmshr}{\textbf{!}} %*12.1 and *12.11, used for predicative propositional functions \newcommand{\pmpred}[2]{#1\pmshr#2} %for predicates (``predicative functions'') of one variable \newcommand{\pmpredd}[3]{#1\pmshr(#2, #3)} %for predicates (``predicative functions'') of two variables \newcommand{\pmpreddd}[4]{#1\pmshr(#2, #3, #4)} %for predicates (``predicative functions'') of three variables \newcommand{\pmpredddd}[5]{#1\pmshr(#2, #3, #4, #5)} %for predicates (``predicative functions'') of four variables \newcommand{\pmpreddddd}[6]{#1\pmshr(#2, #3, #4, #5, #6)} %for predicates (``predicative functions'') of five variables \newcommand{\pmpredddddd}[7]{#1\pmshr(#2, #3, #4, #5, #6, #7)} %for predicates (``predicative functions'') of six variables \newcommand{\pmid}{\mathbin{=}} \newcommand{\pmnid}{\mathrel{\ooalign{$=$\cr\hidewidth\footnotesize\rotatebox[origin=c]{210}{\textbf{/}}\hidewidth\cr}}} %*13.02 \newcommand{\pmiota}{\ooalign{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}\cr\hidewidth\raisebox{.0125em}{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}}\cr\hidewidth\raisebox{.025em}{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}}\cr\hidewidth\raisebox{.0375em}{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}}\cr\hidewidth\raisebox{.05em}{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}}}} %the rotated Greek iota used in definite descriptions \newcommand{\pmdsc}[1]{(\pmiota#1)} %*14.01 \newcommand{\pmthe}[2]{(\pmiota#1)(#2 #1)} %*14.01 \newcommand{\pmtheb}[2]{[(\pmiota#1)(#2 #1)]} %*14.01 \newcommand{\pmDsc}{\pmiota} \newcommand{\pmexists}{\textbf{E}\hspace{.1em}\pmshr} %*14.02 %Classes and relations %Class signs \newcommand{\pmcls}[2]{\pmhat{#1}(#2)} %20.01 \newcommand{\pmclsb}[2]{\pmhat{#1}\{#2\}} %20.01 with curly brackets \newcommand{\pmcin}{\mathop{\boldsymbol{\epsilon}}} %20.02 \newcommand{\pmCls}{\text{Cls}} %20.03 \newcommand{\pmClsn}[1]{\text{Cls}^{#1}} \newcommand{\pmcinn}{\pmnot\pmcin} %20.06 \newcommand{\pmcinc}{\mathop{\ooalign{$\boldsymbol{\subset}$\cr\hidewidth$\hspace{.1em}\boldsymbol{\subset}$\cr\hidewidth$\hspace{.15em}\boldsymbol{\subset}$\cr\hidewidth$\hspace{.2em}\boldsymbol{\subset}$}}} %22.01 \newcommand{\pmccap}{\mathop{\ooalign{\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.1em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.2em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.3em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.4em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.5em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.6em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}}}} %22.02 \newcommand{\pmccup}{\mathop{\ooalign{\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.1em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.2em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.3em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.4em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.5em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.6em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}}}} %22.03 \newcommand{\pmccmp}[1]{\boldsymbol{-}#1} %22.04 \newcommand{\pmcmin}[2]{#1\boldsymbol{-}#2} %22.05 \newcommand{\pmcuni}{\text{\rotatebox[origin=c]{180}{$\Lambda$}}} %24.01 \newcommand{\pmcnull}{\Lambda} %24.02 \newcommand{\pmcexists}{\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}\hspace{-.1em}\mathop{\pmshr}} %24.03 %Relation signs \newcommand{\pmrel}[3]{\pmhat{#1}\pmhat{#2}#3} %21.01 \newcommand{\pmrelb}[3]{\pmhat{#1}\pmhat{#2}\{#3\}} %21.01 \newcommand{\pmrele}[5]{#1\{\pmhat{#2}\pmhat{#3}#4(#2, #3)\}#5} %21.02 \newcommand{\pmrelep}[3]{#1\{#2\}#3} %21.08, 21.081, 21.082, etc. \newcommand{\pmrcmp}[1]{\ooalign{$\hidewidth\raisebox{.25em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\boldsymbol{\pmccmp}$}#1} %23.04 \newcommand{\pmrmin}[2]{#1\mathrel{\ooalign{$\hidewidth\raisebox{.25em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\boldsymbol{\pmccmp}$}}#2} %23.05 \newcommand{\pmruni}{\pmcirc{\text{\rotatebox[origin=c]{180}{$\Lambda$}}}} %25.01 \newcommand{\pmrnull}{\pmcirc{\Lambda}} %25.02 \newcommand{\pmrexists}{\pmcirc{\mathop{\text{\raisebox{.5em}{\rotatebox{180}{E}}}}}\mathop{\pmshr}} %25.03 \newcommand{\pmrinc}{\mathrel{\ooalign{$\hidewidth\boldsymbol{\cdot}\hidewidth$\cr$\boldsymbol{\pmcinc}$}}} %23.01 \newcommand{\pmrcap}{\mathrel{\ooalign{$\hidewidth\raisebox{.3em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\boldsymbol{\pmccap}$}}} %23.02 \newcommand{\pmrcup}{\mathrel{\ooalign{$\hidewidth\raisebox{.1em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\boldsymbol{\pmccup}$}}} %23.03 %Logic of Relations \newcommand{\pmdscf}[2]{#1\textbf{`}#2} %30.01 \newcommand{\pmcnv}[1]{\text{Cnv}\textbf{`}#1} %31.01 \newcommand{\pmCnv}{\text{Cnv}} \newcommand{\pmcrel}[1]{\pmbreve{#1}} %31.02 \newcommand{\pmrrf}[2]{\overrightarrow{#1}\textbf{`}#2} %32.01 \newcommand{\pmRrf}[1]{\overrightarrow{#1}} \newcommand{\pmrrl}[2]{\overleftarrow{#1}\textbf{`}#2} %32.02 \newcommand{\pmRrl}[1]{\overleftarrow{#1}} \newcommand{\pmsg}[1]{\text{sg}\textbf{`}#1} %32.03 \newcommand{\pmSg}{\text{sg}} \newcommand{\pmgs}[1]{\text{gs}\textbf{`}#1} %32.04 \newcommand{\pmGs}{\text{gs}} \newcommand{\pmdm}[1]{\text{D}\textbf{`}#1} %33.01 \newcommand{\pmDm}{\text{D}} \newcommand{\pmcdm}[1]{\text{\rotatebox[origin=c]{180}{D}}\textbf{`}#1} %33.02 \newcommand{\pmCdm}{\text{\rotatebox[origin=c]{180}{D}}} \newcommand{\pmcmp}[1]{C\textbf{`}#1} %33.03 \newcommand{\pmCmp}{C} \newcommand{\pmfld}[1]{F\textbf{`}#1} %33.04 \newcommand{\pmFld}{F} \newcommand{\pmrprd}[2]{{#1}\mathop{|}{#2}} %34.01 \newcommand{\pmRprd}{\mathop{|}} \newcommand{\pmrprdn}[2]{#1^{#2}} %34.02, 34.03, etc. \newcommand{\pmrld}[2]{#1 \boldsymbol{\upharpoonleft} #2} %35.01 \newcommand{\pmrlcd}[2]{#1 \boldsymbol{\upharpoonright} #2} %35.02 \newcommand{\pmrlf}[3]{#1 \boldsymbol{\upharpoonleft} #2 \boldsymbol{\upharpoonright} #3} %35.03 \newcommand{\pmrl}[2]{#1 \boldsymbol{\uparrow} #2} %35.04 \newcommand{\pmrlF}[2]{#1 \mathbin{\ooalign{$\upharpoonright$\cr\hidewidth\rotatebox[origin=c]{180}{\text{$\upharpoonleft$}}\hidewidth\cr}} #2} %36.01 \newcommand{\pmdscff}[2]{#1\textbf{`}\textbf{`}#2} %37.01 \newcommand{\pmdscfr}[2]{#1_{\pmcin}\textbf{`}#2} %37.02 \newcommand{\pmdscfR}[1]{#1_{\pmcin}} \newcommand{\pmdscfcr}[2]{\pmbreve{#1}_{\pmcin}\textbf{`}#2} %37.03 \newcommand{\pmdscfcR}[1]{\pmbreve{#1}_{\pmcin}} \newcommand{\pmdscfff}[2]{#1\textbf{`}\textbf{`}\textbf{`}#2} %37.04 \newcommand{\pmdscfe}[2]{\mathop{\text{E}}\mathop{\pmshr\pmshr}\pmdscff{#1}{#2}} %37.05 \newcommand{\Female}{{\usefont{U}{mvs}{m}{n}\symbol{126}}} %from the Marvosym package \newcommand{\pmop}{\mathop{\text{\Female}}} %38.01, 38.02 \newcommand{\pmopc}[2]{#1 \mathop{\underset{\textbf{''}}{\text{\Female}}} #2} %38.03 %Products and sums of classes of classes or relations \newcommand{\pmccsum}[1]{p\textbf{`}#1} %40.01 \newcommand{\pmccprd}[1]{s\textbf{`}#1} %40.02 \newcommand{\pmcrsum}[1]{\pmcirc{p}\textbf{`}#1} %41.01 \newcommand{\pmcrprd}[1]{\pmcirc{s}\textbf{`}#1} %41.02 \newcommand{\pmrprdd}[2]{{#1}\mathop{||}{#2}} %43.01 \newcommand{\pmRprdd}{\mathop{||}} %Prolegomena to Cardinal Arithmetic %Unit Classes and Couples %Identity and Diversity \newcommand{\pmrid}{I} %50.01 \newcommand{\pmrdiv}{J} %50.02 \newcommand{\pmcunit}[1]{\iota\textbf{`}#1} %51.01 \newcommand{\pmcUnit}{\iota} \newcommand{\pmcunits}[1]{\pmbreve{\iota}\textbf{`}#1} %52.01 %Cardinal numbers \newcommand{\pmcn}[1]{#1} %52.01, 54.01, 54.02, etc. %Ordinal numbers \newcommand{\pmoc}[2]{#1 \boldsymbol{\downarrow} #2} %55.01, 55.02, etc. \newcommand{\pmdn}[1]{\pmcirc{#1}} %56.01 \newcommand{\pmorn}[1]{#1_r} %56.02, 56.03, etc. %Sub-classes, Sub-relations, and Relative Types %Sub-classes \newcommand{\pmscl}[1]{\text{Cl}\textbf{`}#1} %60.01 \newcommand{\pmsCl}{\text{Cl}} \newcommand{\pmscle}[1]{\text{Cl ex}\textbf{`}#1} %60.02 \newcommand{\pmsCle}{\text{Cl ex}} \newcommand{\pmscls}[1]{\text{Cls}\textbf{`}#1} %60.03 \newcommand{\pmsrl}[1]{\text{Rl}\textbf{`}#1} %61.01 \newcommand{\pmsRl}{\text{Rl}} \newcommand{\pmsrle}[1]{\text{Rl ex}\textbf{`}#1} %61.02 \newcommand{\pmsRle}{\text{Rl ex}} \newcommand{\pmsrel}[1]{\text{Rel}\textbf{`}#1} %61.03 \newcommand{\pmRel}{\text{Rel}} \newcommand{\pmReln}[1]{\text{Rel}^{#1}} %61.04 \newcommand{\pmrin}{\mathop{\boldsymbol{\epsilon}}} %62.01 %Relative type symbols \newcommand{\pmrt}[1]{t\textbf{`}#1} %63.01 \newcommand{\pmrti}[2]{t^{#1}\textbf{`}#2} %63.011 \newcommand{\pmrtc}[2]{t_{#1}\textbf{`}#2} %63.02, 63.03, etc. \newcommand{\pmrtri}[2]{t^{#1}\textbf{`}#2} %63.04 \newcommand{\pmrtrc}[2]{t_{#1}\textbf{`}#2} %64.02, 64.021, 64.022, etc. \newcommand{\pmrtrci}[3]{t_{#1}^{\text{ }#2}\textbf{`}#3} %64.03, 64.031, etc. \newcommand{\pmrtric}[3]{{}^{#1}t_{#2}\textbf{`}#3} %64.04, 64.041, etc. \newcommand{\pmrtdi}[2]{#1_{#2}} %65.01 \newcommand{\pmrtdc}[2]{#1(#2)} %65.02 \newcommand{\pmrtdri}[2]{#1_{#2}} %65.03 \newcommand{\pmrtdrc}[2]{#1(#2)} %65.04 %One-many, Many-one, and One-one relations %Similarity relation signs \newcommand{\pmrdc}[2]{#1\boldsymbol{\to}#2} %70.01 \newcommand{\pmsmbar}{\mathrel{\overline{\text{sm}}}} %73.01 \newcommand{\pmsm}{\mathrel{\text{sm}}} %73.02 \newcommand{\pmSM}{\text{sm}} \newcommand{\pmsmarr}{\overrightarrow{{\pmsm}}} \newcommand{\pmonemany}{1\boldsymbol{\to}\pmCls} \newcommand{\pmmanyone}{\pmCls\boldsymbol{\to}1} \newcommand{\pmoneone}{1\boldsymbol{\to}1} %Selections \newcommand{\pmselp}[1]{P_{\small\Delta}\boldsymbol{`}#1} %80.01 \newcommand{\pmSelp}{P_{\Delta}} \newcommand{\pmsele}[1]{\pmcin_{\small\Delta}\boldsymbol{`}#1} \newcommand{\pmSele}{\pmcin_{\Delta}} \newcommand{\pmself}[1]{F_{\small\Delta}\boldsymbol{`}#1} \newcommand{\pmSelf}{F_{\Delta}} \newcommand{\pmexc}{\text{Cls}^2 \mathop{\text{excl}}} %84.01 \newcommand{\pmexcc}[1]{\text{Cl} \mathop{\text{excl}}\textbf{`}#1} %84.02 \newcommand{\pmex}{\text{Cls excl}} \newcommand{\pmexcn}{\text{Cls} \mathop{\text{ex}^2} \mathop{\text{excl}}} %84.03 \newcommand{\pmselc}[2]{#1 \mathrel{\ooalign{\rotatebox[origin=c]{270}{$\boldsymbol{\mapsto}$}}} #2} \newcommand{\pmmultr}{\mathop{\text{Rel}} \mathop{\text{Mult}}} %88.01 \newcommand{\pmmultc}{\mathop{\text{Cls}^2} \mathop{\text{Mult}}} %88.02 \newcommand{\pmmultax}{\mathop{\text{Mult}} \mathop{\text{ax}}} %88.03 %Inductive relations \newcommand{\pmanc}[1]{#1_\pmast} %90.01 \newcommand{\pmancc}[1]{\pmcrel{#1}_\pmast} %90.02 \newcommand{\pmrst}[1]{#1_\text{st}} %91.01 \newcommand{\pmrstm}[2]{#1_{\text{st}#2}} %91.01, see App. B \newcommand{\pmrts}[1]{#1_\text{ts}} %91.02 \newcommand{\pmrtsm}[2]{#1_{\text{ts}#2}} %91.02, see App. B \newcommand{\pmpot}[1]{\text{Pot}\boldsymbol{`}#1} %91.03 \newcommand{\pmpotid}[1]{\text{Potid}\boldsymbol{`}#1} %91.04 \newcommand{\pmpotidm}[2]{\text{Potid}_{#1}\boldsymbol{`}#2} %91.04, see App. B \newcommand{\pmpo}[1]{#1_\text{po}} %91.05 \newcommand{\pmB}{B} %93.01 \newcommand{\pmmin}[1]{\text{min}_{#1}} %93.02 \newcommand{\pmMin}{\text{min}} \newcommand{\pmmax}[1]{\text{max}_{#1}} %93.021 \newcommand{\pmMax}{\text{max}} \newcommand{\pmgen}[1]{\text{gen}\boldsymbol{`}#1} %93.03 \newcommand{\pmGen}{\text{gen}} \newcommand{\pmefr}[2]{#1\pmast#2} %95.05 \newcommand{\pmipr}[2]{I_{#1}\textbf{`}#2} %96.01 \newcommand{\pmjpr}[2]{J_{#1}\textbf{`}#2} %96.02 \newcommand{\pmfr}[2]{\overset{\boldsymbol{\leftrightarrow}}{#1}\textbf{`}#2} %97.01 %Appendix B (*89) \newcommand{\pmancm}[2]{#1_{\pmast#2}} %89.01 \newcommand{\pmrrfanc}[2]{\overrightarrow{#1}_\pmast\textbf{`}#2} %32.01 plus \pmanc \newcommand{\pmrrfancm}[3]{\overrightarrow{#1}_{\pmast#2}\textbf{`}#3} %32.01 plus \pmancm \newcommand{\pmrrlanc}[2]{\overleftarrow{#1}_\pmast\textbf{`}#2} %32.02 plus \pmanc \newcommand{\pmrrlancm}[3]{\overleftarrow{#1}_{\pmast#2}\textbf{`}#3} %32.02 plus \pmancm \newcommand{\pmclso}[3]{\pmhat{#1}_{#2}(#3)} %20.01 but with order subscript \newcommand{\pmclsbo}[3]{\{\pmhat{#1}_{#2}(#3)\}} %20.01 but with order subscript \newcommand{\pmrorderzero}[1]{#1_0} %89.02 \newcommand{\pmrorderm}[2]{#1_{#2}} %89.02 \newcommand{\pmcorderzero}[1]{#1_0} %analogue for classes, cf. 89.131 \newcommand{\pmcorderm}[2]{#1_{#2}} %analogue for classes, cf. 89.131 \newcommand{\pmporderzero}[1]{#1_0} %analogue for properties, cf. introduction to sec. ed. \SVII \newcommand{\pmporderm}[2]{#1_{#2}} %analogue for properties, cf. introduction to sec. ed. \SVII %Volume II %Cardinal arithmetic %Definition and Logical Properties of Cardinal Numbers \newcommand{\pmnc}[1]{\text{Nc}\textbf{`}#1} %100.01 \newcommand{\pmNc}{\text{Nc}} \newcommand{\pmNC}{\text{NC}} %100.02 \newcommand{\pmNCat}[2]{\text{NC}^{#1}({#2})} %102.01 \newcommand{\pmnoc}[1]{\text{N}_0\text{c}\textbf{`}#1} %103.01 \newcommand{\pmNoc}{\text{N}_0\text{c}} \newcommand{\pmNoC}{\text{N}_0\text{C}} %103.02 \newcommand{\pmnca}[2]{\text{N}^{#1}\text{c}\textbf{`}#2} %104.01, 104.011, etc. \newcommand{\pmNca}[1]{\text{N}^{#1}\text{C}} %104.02, 104.021, etc. \newcommand{\pmch}[2]{#1^{(#2)}} %104.03, 104.031, etc. \newcommand{\pmncd}[2]{\text{N}_{#1}\text{c}\textbf{`}#2} %105.01 \newcommand{\pmNcd}[1]{\text{N}_{#1}\text{C}} %105.02, 105.021, etc. \newcommand{\pmcl}[2]{#1_{(#2)}} %105.03, 105.031, etc. \newcommand{\pmncll}[3]{\text{N}_{#1#2}\text{c}\textbf{`}#3} %106.01, 106.012, etc. \newcommand{\pmnchh}[3]{\text{N}^{#1#2}\text{c}\textbf{`}#3} %106.011 \newcommand{\pmncaa}[3]{\text{N}_{#1}{}^{#2}\text{c}\textbf{`}#3} %106.02 \newcommand{\pmncdd}[3]{{}^{#1}\text{N}_{#2}\text{c}\textbf{`}#3} %106.021 \newcommand{\pmNCll}[2]{\text{N}_{#1#2}\text{C}} %106.03 \newcommand{\pmNChh}[2]{\text{N}^{#1#2}\text{C}} \newcommand{\pmcll}[3]{#1_{(#2#3)}} %106.04 \newcommand{\pmchh}[3]{#1^{(#2#3)}} %106.041 \newcommand{\pmncr}[1]{\text{N}_{00}\text{c}\textbf{`}#1} %106.01 %Addition, Multiplication, Exponentiation \newcommand{\pmarsumc}{\mathrel{+}} %110.01 \newcommand{\pmarsumnc}{\mathrel{{+}_{\text{c}}}} %110.02 \newcommand{\pmsmsmb}{\mathrel{\overline{\text{sm}}\;\overline{\text{sm}}}} %111.01 \newcommand{\pmcrp}[2]{\text{Crp}(#1)\textbf{`}#2} %111.02 \newcommand{\pmsmsm}{\mathrel{\text{sm}\;\text{sm}}} %111.03 \newcommand{\pmarsumcc}[1]{\Sigma\textbf{`}#1} %112.01 \newcommand{\pmarsumcnc}[1]{\Sigma\pmNc\textbf{`}#1} %112.02 \newcommand{\pmarprodc}{\times} %113.02 \newcommand{\pmarprodnc}{\times_\text{c}} %113.03 \newcommand{\pmarprodcnc}[1]{\Pi\pmNc\textbf{`}#1} %114.01 \newcommand{\pmarprodcc}[1]{\text{Prod}\textbf{`}#1} %115.01 \newcommand{\pmarcls}{\pmClsn{3}\text{arithm}} %115.02 \newcommand{\pmarexp}[2]{#1 \mathrel{\text{exp}} #2} %116.01 \newcommand{\pmArexp}{\text{exp}} \newcommand{\pmarncexp}[2]{#1^{#2}} %116.02 \newcommand{\pmarg}{\mathrel{\boldsymbol{>}}} %117.01 \newcommand{\pmarl}{\mathrel{\boldsymbol{<}}} %117.04 \newcommand{\pmargeq}{\mathrel{\ooalign{$\boldsymbol{>}$\hidewidth\cr${\hspace{-.4ex}\raise-.75ex\hbox{\rotatebox[origin=c]{-155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}$}}} %117.05 \newcommand{\pmarleq}{\mathrel{\ooalign{$\boldsymbol{<}$\cr\hidewidth${\raise-.75ex\hbox{\rotatebox[origin=c]{155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}\hspace{-.375ex}$}}} %117.06 %Finite and infinite \newcommand{\pmarsubt}[2]{#1 \mathrel{{-}_\text{c}} #2} %119.01 \newcommand{\pmArsubt}{{-}_\text{c}} \newcommand{\pmNCinduct}{\text{NC}\,\text{induct}} %120.01 \newcommand{\pmncinduct}[1]{\text{N}_#1\text{C}\,\text{induct}} %120.011 \newcommand{\pmClsinduct}{\text{Cls}\,\text{induct}} %120.02 \newcommand{\pmclsinduct}[1]{\text{Cls}_{#1}\,\text{induct}} %120.021 \newcommand{\pmInfinax}{\text{Infin}\,\text{ax}} %120.03 \newcommand{\pminfinax}[1]{\text{Infin}\,\text{ax}(#1)} %120.04 \newcommand{\pmspec}[1]{\text{spec}\textbf{`}#1} %120.43 \newcommand{\pmintoo}[2]{P(#1\mathbin{\boldsymbol{-}}#2)} %121.01 \newcommand{\pmIntoo}[2]{(#1\mathbin{\boldsymbol{-}}#2)} %121.01 \newcommand{\pmintoc}[2]{P({#1}\mathbin{\scalebox{1.2}[.7]{$\boldsymbol{\dashv}$}}{#2})} %121.011 \newcommand{\pmIntoc}[2]{({#1}\mathbin{\scalebox{1.2}[.7]{$\boldsymbol{\dashv}$}}{#2})} %121.011 \newcommand{\pmintco}[2]{P({#1}\mathbin{\scalebox{1.2}[.7]{$\boldsymbol{\vdash}$}}{#2})} %121.012 \newcommand{\pmIntco}[2]{({#1}\mathbin{\scalebox{1.2}[.7]{$\boldsymbol{\vdash}$}}{#2})} %121.012 \newcommand{\pmintcc}[2]{P({#1} \mathbin{\ooalign{$\scalebox{1.2}[.7]{$\boldsymbol{\dashv}$}$\hidewidth\cr$\scalebox{1.2}[.7]{$\boldsymbol{\vdash}$}$}} {#2})} %121.013 \newcommand{\pmIntcc}[2]{({#1} \mathbin{\ooalign{$\scalebox{1.2}[.7]{$\boldsymbol{\dashv}$}$\hidewidth\cr$\scalebox{1.2}[.7]{$\boldsymbol{\vdash}$}$}} {#2})} %121.013 \newcommand{\pmintnc}[1]{P_{#1}} %121.02 \newcommand{\pmfinid}[1]{\text{finid}\textbf{`}#1} %121.03 \newcommand{\pmfin}[1]{\text{fin}\textbf{`}#1} %121.031 \newcommand{\pmintt}[2]{#1_{#2}} %121.04 \newcommand{\pmprog}{\text{Prog}} %122.01 \newcommand{\pmaleph}{\boldsymbol{\aleph}} %123.01 \newcommand{\pmsucc}{\text{N}} %123.02 \newcommand{\pmclsrefl}{\text{Cls}\;\text{refl}} %124.01 \newcommand{\pmncrefl}{\text{NC}\;\text{refl}} %124.02 \newcommand{\pmncmult}{\text{NC}\;\text{mult}} %124.03 \newcommand{\pmncind}{\text{NC}\;\text{ind}} %126.01 \newcommand{\pmnocind}[1]{\text{N}_0\text{Cinduct}\textbf{`}#1} \newcommand{\pmNocind}{\text{N}_0\text{Cinduct}} %Relation-arithmetic %Ordinal similarity and relation-numbers \newcommand{\pmrnsm}[2]{{#1}{\raise.4ex\hbox{\textbf{\large;}}}{#2}} %150.01 \newcommand{\pmrnsmd}[2]{#1 \mathop{\boldsymbol{\dagger}} #2} %150.02 \newcommand{\pmrnsmdf}[1]{#1\boldsymbol{\dagger}} \newcommand{\pmopsc}[2]{#1 \mathrel{\ooalign{${\raise-.7ex\hbox{$\pmdot$}}$\hidewidth\cr$\text{\Female}$\hidewidth\cr${\raise-.8ex\hbox{\hspace{.15cm}\textbf{,}}}$}} #2} %150.03 \newcommand{\pmsmorb}[2]{#1 \mathrel{\overline{\text{smor}}} #2} %151.01 \newcommand{\pmSmorb}{\overline{\text{smor}}} %151.01 \newcommand{\pmsmor}[2]{#1 \mathrel{\text{smor}} #2} %151.02 \newcommand{\pmSmor}{\text{smor}} \newcommand{\pmnr}[1]{\text{Nr}\textbf{`}#1} %152.01 \newcommand{\pmNr}{\text{Nr}} \newcommand{\pmNR}{\text{NR}} %152.02 \newcommand{\pmsrrn}[1]{{#1}_{s}} %153.01 \newcommand{\pmNRat}[2]{\text{NR}^{#1}({#2})} %154.01 \newcommand{\pmnor}[1]{\text{N}_0\text{r}\textbf{`}#1} %155.01 \newcommand{\pmNor}{\text{N}_0\text{r}} \newcommand{\pmNoR}{\text{N}_0\text{R}} %155.02 %Addition of Relations, and the Product of Two Relations \newcommand{\pmrsum}[2]{#1\mathrel{\ooalign{${\raise-.21ex\hbox{$\boldsymbol{-}$}}$\cr\hidewidth$\boldsymbol{\uparrow}$\hidewidth\cr${\raise-.19ex\hbox{$\boldsymbol{-}$}}$}} #2} %160.01 \newcommand{\pmRsum}{\mathrel{\ooalign{${\raise-.21ex\hbox{$\boldsymbol{-}$}}$\cr\hidewidth$\boldsymbol{\uparrow}$\hidewidth\cr${\raise-.19ex\hbox{$\boldsymbol{-}$}}$}}} \newcommand{\pmrsume}[2]{#1 \mathrel{\rotatebox[origin=c]{90}{$\pmRsum$}} #2} %161.01 \newcommand{\pmRsume}{\rotatebox[origin=c]{90}{$\pmRsum$} } \newcommand{\pmrsumb}[2]{#1 \mathrel{\rotatebox[origin=c]{270}{$\pmRsum$}} #2} %161.02 \newcommand{\pmRsumb}{\rotatebox[origin=c]{270}{$\pmRsum$}} \newcommand{\pmrsumr}[1]{\Sigma\textbf{`}#1} %162.01 \newcommand{\pmRsumr}{\Sigma} \newcommand{\pmrsumrex}[1]{\mathrel{\text{Rel}^{#1}\text{excl}}} %163.01 \newcommand{\pmsmorsmorb}[2]{#1 \mathrel{\overline{\text{smor}}\,\overline{\text{smor}}} #2} %164.01 \newcommand{\pmSmorsmorb}{\overline{\text{smor}}\,\overline{\text{smor}}} \newcommand{\pmsmorsmor}[2]{#1 \mathrel{\pmSmor\,\pmSmor} #2} %164.02 \newcommand{\pmSmorsmor}{\pmSmor\,\pmSmor} \newcommand{\pmrprod}[2]{#1 \times #2} %166.01 %First differences and the multiplication and exponentiation of relations %On the relation of first differences among the sub-classes of a given class \newcommand{\pmrfdcl}[3]{#2 \mathrel{#1_{\text{cl}}} #3} %170.01 \newcommand{\pmRfdcl}[1]{#1_{\text{cl}}} \newcommand{\pmrfdlc}[3]{#2 \mathrel{#1_{\text{lc}}} #3} %170.02 \newcommand{\pmRfdlc}[1]{#1_{\text{lc}}} \newcommand{\pmrfddf}[3]{#2 \mathrel{#1_{\text{df}}} #3} %171.01 \newcommand{\pmRfddf}[1]{#1_{\text{df}}} \newcommand{\pmrfdfd}[3]{#2 \mathrel{#1_{\text{fd}}} #3} %171.02 \newcommand{\pmRfdfd}[1]{#1_{\text{fd}}} \newcommand{\pmrfprod}[1]{\Pi\textbf{`}#1} %172.01 \newcommand{\pmRfprod}[1]{\text{Prod}\textbf{`}#1} %173.01 \newcommand{\pmrarrel}[1]{\mathrel{\text{Rel}^{#1}\text{arithm}}} %174.01 \newcommand{\pmrexp}{\mathrel{\text{exp}}} %176.01 \newcommand{\pmRexp}[2]{{#1}^{#2}} %176.02 \newcommand{\pmrnsum}[2]{{#1} + {#2}} %180.01 \newcommand{\pmRnsum}{+} \newcommand{\pmrndsum}[2]{{#1} \mathrel{\pmcirc{+}} {#2}} %180.02 \newcommand{\pmRndsum}{\pmcirc{+}} \newcommand{\pmrnsumru}[2]{#1 \mathrel{\pmcirc{\pmRsumb}} #2} %181.01 \newcommand{\pmRnsumru}{\pmcirc{\pmRsumb}} \newcommand{\pmrnsumur}[2]{#1 \mathrel{\pmcirc{\pmRsume}} #2} %181.011 \newcommand{\pmRnsumur}{\pmcirc{\pmRsume}} \newcommand{\pmrn}[1]{\pmcirc{#1}} %181.02 \newcommand{\pmrsep}[1]{\ooalign{${\raise1.5ex\hbox{\rotatebox[origin=c]{180}{\scalebox{1.4}[1.4]{$\pmbreve{\phantom{.}}$}}}}$\cr\hidewidth$#1$\hidewidth}} %182.01 \newcommand{\pmrnsumf}[1]{\Sigma\pmNr\textbf{`}#1} %183.01 \newcommand{\pmrnprod}[2]{#1 \mathrel{\pmcirc{\times}} #2} %184.01 \newcommand{\pmRnprod}{\pmcirc{\times}} \newcommand{\pmrnprodf}[1]{\Pi\pmNr\textbf{`}#1} %185.01 \newcommand{\pmrnexp}[3]{#2 \mathrel{\pmArexp_{#1}} #3} %186.01 \newcommand{\pmRnexp}[1]{\pmArexp_{#1}} %Series %General theory of series \newcommand{\pmtrans}{\text{trans}} %201.01 \newcommand{\pmconnex}{\text{connex}} %202.01 \newcommand{\pmser}{\text{Ser}} %204.01 \newcommand{\pmseq}[3]{#1 \mathrel{\text{seq}_{#1}} #2} %206.01 \newcommand{\pmSeq}[1]{\text{seq}_{#1}} \newcommand{\pmprec}[3]{#1 \mathrel{\text{prec}_{#1}} #2} %206.02 \newcommand{\pmPrec}[1]{\text{prec}_{#1}} \newcommand{\pmlt}[1]{\text{lt}_{#1}} %207.01 \newcommand{\pmtl}[1]{\text{tl}_{#1}} %207.01 \newcommand{\pmlimax}[2]{\text{limax}_{#1}\textbf{`}#2} %207.03 \newcommand{\pmLimax}[1]{\text{limax}_{#1}} \newcommand{\pmlimin}[2]{\text{limin}_{#1}\textbf{`}#2} %207.04 \newcommand{\pmLimin}[1]{\text{limin}_{#1}} \newcommand{\pmcr}[1]{\text{cr}\textbf{`}{#1}} \newcommand{\pmCr}{\text{cr}} \newcommand{\pmcror}[1]{\text{cror}\textbf{`}{#1}} %208.01 \newcommand{\pmCror}{\text{cror}} %On sections, segments, stretches, and derivatives \newcommand{\pmsect}[1]{\text{sect}\textbf{`}{#1}} %211.01 \newcommand{\pmSect}{\text{sect}} \newcommand{\pmseg}[1]{\boldsymbol{\varsigma}\textbf{`}{#1}} %212.01 \newcommand{\pmSeg}{\boldsymbol{\varsigma}} \newcommand{\pmsym}[1]{\text{sym}\textbf{`}{#1}} %212.02 \newcommand{\pmSym}{\text{sym}} \newcommand{\pmsectr}[1]{{#1}_{\pmSeg}} %213.01 \newcommand{\pmded}{\mathrel{\text{Ded}}} %214.01 \newcommand{\pmsded}{\mathrel{\text{semi}\;\text{Ded}}} %214.02 \newcommand{\pmstr}[1]{\text{str}\textbf{`}{#1}} %215.01 \newcommand{\pmStr}{\text{str}} \newcommand{\pmder}[2]{\delta_{#1}\textbf{`}#2} %216.01 \newcommand{\pmDer}[1]{\delta_{#1}} \newcommand{\pmdern}[3]{\delta_{#1}^{#2}\textbf{`}#3} \newcommand{\pmden}[1]{\text{dense}\textbf{`}{#1}} %216.02 \newcommand{\pmDen}{\text{dense}} \newcommand{\pmclsd}[1]{\text{closed}\textbf{`}{#1}} %216.03 \newcommand{\pmClsd}{\text{closed}} \newcommand{\pmperf}[1]{\text{perf}\textbf{`}{#1}} %216.04 \newcommand{\pmPerf}{\text{perf}} \newcommand{\pmders}[1]{\rotatebox[origin=c]{180}{$\Delta$}\textbf{`}#1} %216.05 \newcommand{\pmDers}{\rotatebox[origin=c]{180}{$\Delta$}} %On convergence, and the limits of functions \newcommand{\pmconv}[3]{#1\bar{#2}_{\text{cn}}#3} %230.01 \newcommand{\pmConv}[1]{{#1}_{\text{cn}}} %230.02 \newcommand{\pmconvg}[3]{#1\bar{#2}_{\text{cng}}#3} \newcommand{\pmConvg}[1]{{#1}_{\text{cng}}} \newcommand{\pmlsc}[3]{#1\bar{#2}_{\text{sc}}#3} %231.01 \newcommand{\pmosc}[3]{#1\bar{#2}_{\text{os}}#3} %231.02 \newcommand{\pmlscl}[4]{(#1\bar{#2}#3)_{\text{sc}}\textbf{`}#4} %232.01 \newcommand{\pmoscl}[4]{(#1\bar{#2}#3)_{\text{os}}\textbf{`}#4} %232.02 \newcommand{\pmlmx}[4]{(#1\bar{#2}#3)_{\text{lmx}}\textbf{`}#4} %233.01 \newcommand{\pmLmx}[3]{(#1\bar{#2}#3)_{\text{lmx}}} \newcommand{\pmlimf}[4]{#1(#2#3)\textbf{`}#4} %233.02 \newcommand{\pmLimf}[3]{#1(#2#3)} \newcommand{\pmscf}[3]{\text{sc}(#1, #2)\boldsymbol{`}#3} %234.01 \newcommand{\pmosf}[3]{\text{os}(#1, #2)\boldsymbol{`}#3} %234.02 \newcommand{\pmctf}[3]{\text{ct}(#1#2)\boldsymbol{`}#3} %234.03 \newcommand{\pmcontinf}[3]{\text{contin}(#1#2)\boldsymbol{`}#3} %234.04 \newcommand{\pmcontin}[2]{#1 \mathrel{\text{contin}} #2} %234.05 \newcommand{\pmContin}{\text{contin}} %Volume III %Well-Ordered Series \newcommand{\pmbord}{\text{Bord}} %250.01 \newcommand{\pmword}{\Omega} %250.02 \newcommand{\pmordn}{\text{NO}} %251.01 \newcommand{\pmless}{\mathrel{\text{less}}} %254.01 \newcommand{\pmLess}{\text{less}} \newcommand{\pmpsc}[2]{#1 \mathrel{P_{\text{sm}}} #2} %254.02 \newcommand{\pmPsc}{P_{\text{sm}}} \newcommand{\pmorle}{\mathrel{\ooalign{$\boldsymbol{<}$\cr\hidewidth$\boldsymbol{\cdot}$}}} %255.01 \newcommand{\pmorgr}{\mathrel{\ooalign{$\boldsymbol{>}$\hidewidth\cr$\boldsymbol{\cdot}$\hidewidth}}} %255.02 \newcommand{\pmnoo}{\text{N}_0\text{O}} %255.03 \newcommand{\pmorleq}{\mathrel{\ooalign{$\boldsymbol{<}$\cr\hidewidth$\boldsymbol{\cdot}$\cr\hidewidth${\raise-.75ex\hbox{\rotatebox[origin=c]{155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}\hspace{-.375ex}$}}} %255.04 \newcommand{\pmorgrq}{\mathrel{\ooalign{$\boldsymbol{>}$\hidewidth\cr$\boldsymbol{\cdot}$\hidewidth\cr${\hspace{-.4ex}\raise-.75ex\hbox{\rotatebox[origin=c]{-155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}$\hidewidth}}} %255.05 \newcommand{\pmm}{\emph{M}} %256.01 \newcommand{\pmn}{\emph{N}} %256.02, 263.02 \newcommand{\pmtranc}[3]{(#1\pmast#2)\textbf{`}#3} %257.01 \newcommand{\pmTranc}[2]{(#1\pmast#2)} %257.01 \newcommand{\pmtrpot}[3]{#1_{#2#3}} %257.02 \newcommand{\pma}{\emph{A}} %259.01 \newcommand{\pmaw}{\emph{A}_{\emph{W}}} %259.02 \newcommand{\pmwa}{\emph{W}_{\emph{A}}} %259.03 %Finite and Infinite Series and Ordinals \newcommand{\pmintf}{P_{\text{fn}}} %260.01 \newcommand{\pmserinf}{\text{Ser infin}} %261.01 \newcommand{\pmwordinf}{\pmword\text{ infin}} %261.02 \newcommand{\pmserfin}{\text{Ser fin}} %261.03 \newcommand{\pmwordfin}{\pmword\text{ fin}} %261.04 \newcommand{\pmwordind}{\pmword\text{ induct}} %261.04 \newcommand{\pmordnfin}{\text{NO fin}} %262.01 \newcommand{\pmordninf}{\text{NO infin}} %262.02 \newcommand{\pmfinord}[1]{#1_r} %262.03 \newcommand{\pmom}{\boldsymbol{\omega}} %263.01 \newcommand{\pmpr}[1]{#1_{\text{pr}}} %264.01 \newcommand{\pmomn}[1]{\pmom_{#1}} %265.01, 265.03, etc. \newcommand{\pmalephn}[1]{\pmaleph_{#1}} %265.02, 265.04, etc. %Compact series, rational series, and continuous series \newcommand{\pmcomp}{\mathrel{\text{comp}}} %270.01 \newcommand{\pmComp}{\text{Comp}} \newcommand{\pmmed}{\mathrel{\text{med}}} %271.01 \newcommand{\pmMed}{\text{med}} \newcommand{\pmsimp}[3]{\mathrel{#1_{#2#3}}} %272.01 \newcommand{\pmsimps}[3]{{#1}_{#2}\textbf{`}{#3}} %273.02 \newcommand{\pmSimp}[3]{({#1}{#2})_{#3}} %273.03 \newcommand{\pmSimps}[2]{{#1}_{#2}} %273.04 \newcommand{\pmrats}{\eta} %273.01 \newcommand{\pmsfcls}[1]{#1_\pmrats} %274.01 \newcommand{\pmsfclsm}[2]{#1_m\textbf{`}#2} %274.02 \newcommand{\pmsfclsp}[2]{\pmbreve{#1}_P\textbf{`}{#2}} %274.03 \newcommand{\pmsfclsmp}[1]{M_P\textbf{`}{#1}} %274.04 \newcommand{\pmcser}{\theta} %275.01 \newcommand{\pmcsercl}[1]{#1_\pmcser} %276.01 \newcommand{\pmcsercls}[2]{{#1}_{#2}} %276.04 \newcommand{\pmCsercls}[2]{{#1}_{\text{tl}}\textbf{`}{#2}} %264.05 %Skipped some temprary definitions as repetitious %Quantity %Generalization of Number \newcommand{\pmu}{\textit{U}} %300.01 \newcommand{\pmrnum}{\text{Rel num}} %300.02 \newcommand{\pmrnumid}{\text{Rel num id}} %300.03 \newcommand{\pmrpwr}[2]{#1^#2} %301.03 \newcommand{\pmPrm}{\text{Prm}} %302.01 \newcommand{\pmrprm}[4]{(#1,#2)\mathbin{\pmPrm_\tau}(#3,#4)} %302.02 \newcommand{\pmprm}[4]{(#1,#2)\mathbin{\pmPrm}(#3,#4)} %302.03 \newcommand{\pmhcf}[2]{\text{hcf}(#1,#2)} %302.04 \newcommand{\pmHcf}{\text{hcf}} \newcommand{\pmlcm}[2]{\text{lcm}(#1,#2)} %302.05 \newcommand{\pmLcm}{\text{lcm}} \newcommand{\pmrat}[2]{#1 \rotatebox[origin=c]{10}{$\boldsymbol{/}$} #2} %303.01 \newcommand{\pmqn}[1]{#1_q} %303.02 \newcommand{\pmqnil}{\infty_q} %303.03 \newcommand{\pmRat}{\text{Rat}} %303.04 \newcommand{\pmRatdef}{\text{Rat def}} %303.05 \newcommand{\pmqnle}[2]{#1 \mathrel{\boldsymbol{<}_r} #2} %304.01 \newcommand{\pmQnle}{\boldsymbol{<}_r} \newcommand{\pmqnLe}{H} %304.02 \newcommand{\pmqnlez}{H'} %304.03 \newcommand{\pmprodsr}[2]{#1 \times_s #2} %305.01 \newcommand{\pmProdsr}{\times_s} \newcommand{\pmsumsr}[2]{#1 +_s #2} %306.01 \newcommand{\pmSumsr}{+_s} \newcommand{\pmratn}{\text{Rat}_n} %307.01 \newcommand{\pmratg}{\text{Rat}_g} %307.011 \newcommand{\pmratnle}[2]{#1 \mathrel{\boldsymbol{<}_n} #2} %307.02 \newcommand{\pmRatnle}{\boldsymbol{<}_n} \newcommand{\pmatngr}[2]{#1 \mathrel{\boldsymbol{>}_n} #2} %307.021 \newcommand{\pmRatngr}{\boldsymbol{>}_n} \newcommand{\pmratgle}[2]{#1 \mathrel{\boldsymbol{<}_g} #2} %307.03 \newcommand{\pmRatgle}{\boldsymbol{<}_g} \newcommand{\pmratggr}[2]{#1 \mathrel{\boldsymbol{>}_g} #2} %307.031 \newcommand{\pmRatggr}{\boldsymbol{>}_g} \newcommand{\pmratnLe}{H_n} %307.04 \newcommand{\pmratgLe}{H_g} %307.05 \newcommand{\pmratssub}[2]{#1 \boldsymbol{-}_s #2} %308.01 \newcommand{\pmsumgr}[2]{#1 +_g #2} %308.02 \newcommand{\pmprodgr}[2]{#1 \times_g #2} %309.01 \newcommand{\pmrenp}{\Theta} %310.01 \newcommand{\pmrenpz}{\Theta'} %310.011 \newcommand{\pmrenn}{\Theta_n} %310.02 \newcommand{\pmrennz}{\Theta_n'} %310.021 \newcommand{\pmreng}{\Theta_g} %310.03 \newcommand{\pmconc}[1]{\text{concord}(#1)} %311.01 \newcommand{\pmConc}{\text{concord}} \newcommand{\pmrensumc}[2]{#1 +_p #2} %311.02 \newcommand{\pmrensub}[2]{#1 -_p #2} %312.01 \newcommand{\pmrensuma}[2]{#1 +_a #2} %312.02 \newcommand{\pmrenproda}[2]{#1 \times_a #2} %313.01 \newcommand{\pmrenrsum}[2]{#1 +_r #2} %314.01 \newcommand{\pmrenrprod}[2]{#1 \times_r #2} %314.02 \newcommand{\Male}{{\usefont{U}{mvs}{m}{n}\symbol{124}}} %from the Marvosym package \newcommand{\pmrenr}{\mathop{\text{\Male}}} %314.03 \newcommand{\pmrenrssum}[2]{#1 +_\sigma #2} %314.04 \newcommand{\pmrenrsprod}[2]{#1 \times_\sigma #2} %313.05 %Vector Families \newcommand{\pmcorr}[1]{\text{cr}\textbf{`}#1} %330.01 \newcommand{\pmabel}{\text{Abel}} %330.02 \newcommand{\pmvfm}[1]{\text{fm}\textbf{`}#1} %330.03 \newcommand{\pmVfm}{\text{fm}} \newcommand{\pmvfmcl}{\textit{FM}} %330.04 \newcommand{\pmvffb}[1]{#1_\iota} %330.05 \newcommand{\pmconx}[1]{\text{conx}\textbf{`}#1} %331.01 \newcommand{\pmconxfm}{\textit{FM}\text{ conx}} %331.02 \newcommand{\pmfrep}[2]{\text{rep}_#1\textbf{`}#2} %332.01 \newcommand{\pmfopen}[1]{#1_\partial} %333.01 \newcommand{\pmfopennid}[1]{#1_{\iota\partial}} %333.011 \newcommand{\pmfmap}{\textit{FM}\text{ ap}} %333.02 \newcommand{\pmfmapconx}{\textit{FM}\text{ ap conx}} %333.03 \newcommand{\pmtrsp}[1]{\text{trs}\textbf{`}#1} %334.01 \newcommand{\pmfmtrs}{\textit{FM}\text{ trs}} %334.02 \newcommand{\pmfmconnex}{\textit{FM}\text{ connex}} %334.03 \newcommand{\pmfmsr}{\textit{FM}\text{ sr}} %334.02 \newcommand{\pmfmasym}{\textit{FM}\text{ asym}} %334.05 \newcommand{\pminit}[1]{\text{init}\textbf{`}#1} %335.01 \newcommand{\pmfminit}{\textit{FM}\text{ init}} %335.02 \newcommand{\pmvr}[1]{\textit{V}_#1} %336.01 \newcommand{\pmvrnid}[1]{\textit{U}_#1} %336.011 \newcommand{\pmarvs}[1]{A_{#1}} %336.02 %Measurement \newcommand{\pmfmsubm}{\textit{FM}\text{ subm}} %351.01 \newcommand{\pmvrm}[2]{#1_#2} %352.01 \newcommand{\pmvrmg}[2]{#1_{#2\iota}} %352.02 \newcommand{\pmfmrt}{\textit{FM}\text{ rt}} %353.01 \newcommand{\pmfmcx}{\textit{FM}\text{ cx}} %353.02 \newcommand{\pmfmrtcx}{\textit{FM}\text{ rt cx}} %353.03 \newcommand{\pmfmg}[1]{#1_g} %354.01 \newcommand{\pmrtnet}[2]{\text{cx}_#1\textbf{`}#2} %354.02 \newcommand{\pmfmgrp}{\textit{FM}\text{ grp}} %354.03 \newcommand{\pmrems}[2]{#1_#2} %356.01 %Cyclic Families \newcommand{\pmfmcycl}{\textit{FM}\text{ cycl}} %370.01 \newcommand{\pmcycl}[2]{#1_#2} %370.02 \newcommand{\pmcycli}[2]{#1_#2} %370.03 \newcommand{\pmvser}[2]{#1_#2} %371.01 \newcommand{\pmintsecvser}[2]{#1_#2} %372.01 \newcommand{\pmprime}{\text{Prime}} %373.01 \newcommand{\pmsfmid}[3]{#1_{#2#3}} %373.02 \newcommand{\pmsmltid}[2]{(#1, #2)} %373.03 \newcommand{\pmprrt}[3]{(#1 \rotatebox[origin=c]{10}{$\boldsymbol{/}$} #2)_{#3}} %375.01 \begin{document} \chapter*{\centering LIST OF DEFINITIONS} \onehalfspacing \begin{tabular}{l l} \text{ }$\pmast1\pmcdot01$. & $p \pmimp q$ \\ \text{ }$\pmast2\pmcdot33$. & $p \pmor q \pmor r$ \\ \text{ }$\pmast3\pmcdot01$. & $p \pmand q$ \\ \text{ }$\pmast3\pmcdot02$. & $p \pmimp q \pmimp r$ \\ \text{ }$\pmast4\pmcdot01$. & $p \pmiff q$ \\ \text{ }$\pmast4\pmcdot02$. & $p \pmiff q \pmiff r$ \\ \text{ }$\pmast4\pmcdot34$. & $p \pmand q \pmand r$ \\ \text{ }$\pmast9\pmcdot01$. & $\pmnot\{\pmall{x}\pmdot \phi x\}$ \\ \text{ }$\pmast9\pmcdot011$. & $\pmnot\pmall{x}\pmdot \phi x$ \\ \text{ }$\pmast9\pmcdot02$. & $\pmnot\{\pmsome{x}\pmdot \phi x\}$ \\ \text{ }$\pmast9\pmcdot021$. & $\pmnot\pmsome{x}\pmdot \phi x$ \\ \text{ }$\pmast9\pmcdot03$. & $\pmall{x}\pmdot \phi x \pmdot \pmor \pmdot p$ \\ \text{ }$\pmast9\pmcdot04$. & $p \pmdot \pmor \pmdot \pmall{x}\pmdot \phi x$ \\ \text{ }$\pmast9\pmcdot05$. & $\pmsome{x}\pmdot \phi x \pmdot \pmor \pmdot p$ \\ \text{ }$\pmast9\pmcdot06$. & $p \pmdot \pmor \pmdot \pmsome{x}\pmdot \phi x$ \\ \text{ }$\pmast9\pmcdot07$. & $\pmall{x}\pmdot \phi x \pmdot \pmor \pmdot \pmsome{y}\pmdot \psi y$ \\ \text{ }$\pmast9\pmcdot08$. & $\pmsome{y}\pmdot \psi y \pmdot \pmor \pmdot \pmall{x}\pmdot \phi x$ \\ $\pmast10\pmcdot01$. & $\pmsome{x}\pmdot \phi x$ \\ $\pmast10\pmcdot02$. & $\phi x \pmimp_x \psi x$ \\ $\pmast10\pmcdot03$. & $\phi x \pmiff_x \psi x$ \\ $\pmast11\pmcdot01$. & $\pmall{x,y}\pmdot \phi(x, y)$ \\ $\pmast11\pmcdot02$. & $\pmall{x,y,z}\pmdot \phi(x, y, z)$ \\ $\pmast11\pmcdot03$. & $\pmsome{x,y}\pmdot \phi(x, y)$ \\ $\pmast11\pmcdot04$. & $\pmsome{x,y,z}\pmdot \phi(x, y, z)$ \\ $\pmast11\pmcdot05$. & $\phi(x, y) \pmdot\pmimp_{x, y}\pmdot \psi(x, y)$ \\ $\pmast11\pmcdot06$. & $\phi(x, y) \pmdot\pmiff_{x, y}\pmdot \psi(x, y)$ \\ $\pmast13\pmcdot01$. & $x = y$ \\ $\pmast13\pmcdot02$. & $x \pmnid y$ \end{tabular} \begin{tabular}{l l} $\pmast13\pmcdot03$. & $x = y = z$ \\ $\pmast14\pmcdot01$. & $[\pmdsc{x}(\phi x)]\pmdot \psi\pmdsc{x}(\phi x)$ \\ $\pmast14\pmcdot02$. & $\pmexists\pmdsc{x}(\phi x)$ \\ $\pmast14\pmcdot03$. & $[\pmdsc{x}(\phi x), \pmdsc{x}(\psi x)]\pmdot f\{\pmdsc{x}(\phi x),$\\ & \indent $\pmdsc{x}(\psi x)\}$ \\ $\pmast14\pmcdot04$. & $[\pmdsc{x}(\psi x)]\pmdot f\{\pmdsc{x}(\phi x), \pmdsc{x}(\psi x)\}$ \\ $\pmast20\pmcdot01$. & $f\{\pmcls{z}{\psi z}\}$ \\ $\pmast20\pmcdot02$. & $x \mathrel{\pmcin} (\pmpred{\phi}{\pmhat{z}})$ \\ $\pmast20\pmcdot03$. & $\pmCls$ \\ $\pmast20\pmcdot04$. & $x, y \pmcin \alpha$ \\ $\pmast20\pmcdot05$. & $x, y, z \pmcin \alpha$ \\ $\pmast20\pmcdot06$. & $x \pmnot \pmcin \alpha$ \\ $\pmast20\pmcdot07$. & $\pmall{\alpha}\pmdot f\alpha$ \\ $\pmast20\pmcdot071$. & $\pmsome{\alpha}\pmdot f\alpha$ \\ $\pmast20\pmcdot072$. & $[\pmdsc{\alpha}(\phi \alpha)]\pmdot f\pmdsc{\alpha}(\phi \alpha)$ \\ $\pmast20\pmcdot08$. & $f\{\pmcls{\alpha}{\psi \alpha}\}$ \\ $\pmast20\pmcdot081$. & $\alpha \pmcin \pmpred{\psi}{\alpha}$ \\ $\pmast21\pmcdot01$. & $f\{\pmrel{x}{y}{\psi(x,y)}\}$ \\ $\pmast21\pmcdot02$. & $\pmrelep{a}{\pmpredd{\phi}{\pmhat{x}}{\pmhat{y}}}{b}$ \\ $\pmast21\pmcdot03$. & $\pmRel$ \\ $\pmast21\pmcdot07$. & $\pmall{R}\pmdot fR$ \\ $\pmast21\pmcdot071$. & $\pmsome{R}\pmdot fR$ \\ $\pmast21\pmcdot072$. & $[\pmdsc{R}(\phi R)]\pmdot f\pmdsc{R}(\phi R)$ \\ $\pmast21\pmcdot08$. & $f\{\pmrel{R}{S}{\psi(R, S)}\}$ \\ $\pmast21\pmcdot081$. & $\pmrelep{P}{\pmpredd{\phi}{\pmhat{R}}{\pmhat{S}}}{Q}$ \\ $\pmast21\pmcdot082$. & $f\{\pmcls{R}{\psi R}\}$ \\ $\pmast21\pmcdot083$. & $R \pmcin \pmpred{\phi}{\pmhat{R}}$ \\ $\pmast22\pmcdot01$. & $\alpha \pmcinc \beta$ \\ $\pmast22\pmcdot02$. & $\alpha \pmccap \beta$ \end{tabular} \begin{tabular}{l l} $\pmast22\pmcdot03$. & $\alpha \pmccup \beta$ \\ $\pmast22\pmcdot04$. & $\pmccmp{\alpha}$ \\ $\pmast22\pmcdot05$. & $\pmcmin{\alpha}{\beta}$ \\ $\pmast22\pmcdot53$. & $\alpha \pmccap \beta \pmccap \gamma$ \\ $\pmast22\pmcdot71$. & $\alpha \pmccup \beta \pmccup \gamma$ \\ $\pmast23\pmcdot01$. & $R \pmrinc S$ \\ $\pmast23\pmcdot02$. & $R \pmrcap S$ \\ $\pmast23\pmcdot03$. & $R \pmrcup S$ \\ $\pmast23\pmcdot04$. & $\pmrcmp{R}$ \\ $\pmast23\pmcdot05$. & $\pmrmin{R}{S}$ \\ $\pmast23\pmcdot53$. & $R \pmrcap S \pmrcap T$ \\ $\pmast23\pmcdot71$. & $R \pmrcup S \pmrcup T$ \\ $\pmast24\pmcdot01$. & $\pmcuni$ \\ $\pmast24\pmcdot02$. & $\pmcnull$ \\ $\pmast24\pmcdot03$. & $\pmcexists \alpha$ \\ $\pmast25\pmcdot01$. & $\pmruni$ \\ $\pmast25\pmcdot02$. & $\pmrnull$ \\ $\pmast25\pmcdot03$. & $\pmrexists R$ \\ $\pmast30\pmcdot01$. & $\pmdscf{R}{y}$ \\ $\pmast30\pmcdot02$. & $\pmdscf{R}{\pmdscf{S}{y}}$ \\ $\pmast31\pmcdot01$. & $\pmCnv$ \\ $\pmast31\pmcdot02$. & $\pmcrel{P}$ \\ $\pmast32\pmcdot01$. & $\pmRrf{R}$ \\ $\pmast32\pmcdot02$. & $\pmRrl{R}$ \\ $\pmast32\pmcdot03$. & $\pmSg$ \\ $\pmast32\pmcdot04$. & $\pmGs$ \\ $\pmast33\pmcdot01$. & $\pmDm$ \\ $\pmast33\pmcdot02$. & $\pmCdm$ \\ $\pmast33\pmcdot03$. & $\pmCmp$ \\ $\pmast33\pmcdot04$. & $\pmFld$ \\ $\pmast34\pmcdot01$. & $\pmrprd{R}{S}$ \\ $\pmast34\pmcdot02$. & $\pmrprdn{R}{2}$ \end{tabular} \begin{tabular}{l l} $\pmast34\pmcdot03$. & $\pmrprdn{R}{3}$ \\ $\pmast35\pmcdot01$. & $\pmrld{\alpha}{R}$ \\ $\pmast35\pmcdot02$. & $\pmrlcd{R}{\beta}$ \\ $\pmast35\pmcdot03$. & $\pmrlf{\alpha}{R}{\beta}$ \\ $\pmast35\pmcdot04$. & $\pmrl{\alpha}{\beta}$ \\ $\pmast35\pmcdot05$. & $\pmrl{\pmdscf{R}{x}}{\beta}$ \\ $\pmast35\pmcdot24$. & $\pmrld{\alpha}{\pmrprd{R}{S}}$ \\ $\pmast35\pmcdot25$. & $\pmrlcd{\pmrprd{S}{R}}{\alpha}$ \\ $\pmast36\pmcdot01$. & $\pmrlF{P}{\alpha}$ \\ $\pmast37\pmcdot01$. & $\pmdscff{R}{\beta}$ \\ $\pmast37\pmcdot02$. & $\pmdscfR{R}$ \\ $\pmast37\pmcdot03$. & ${\pmdscfR{\pmcrel{R}}}$\\ $\pmast37\pmcdot04$. & $\pmdscfff{R}{\kappa}$ \\ $\pmast37\pmcdot05$. & $\pmdscfe{R}{\beta}$ \\ $\pmast38\pmcdot01$. & $x \pmop$ \\ $\pmast38\pmcdot02$. & $\pmop y$ \\ $\pmast38\pmcdot03$. & $\pmopc{\alpha}{y}$\\ $\pmast40\pmcdot01$. & $\pmccsum{\kappa}$ \\ $\pmast40\pmcdot02$. & $\pmccprd{\kappa}$ \\ $\pmast41\pmcdot01$. & $\pmcrsum{\lambda}$ \\ $\pmast41\pmcdot02$. & $\pmcrprd{\lambda}$ \\ $\pmast43\pmcdot01$. & $\pmrprdd{R}{S}$ \\ $\pmast50\pmcdot01$. & $\pmrid$ \\ $\pmast50\pmcdot02$. & $\pmrdiv$ \\ $\pmast51\pmcdot01$. & $\pmcUnit$ \\ $\pmast52\pmcdot01$. & $\pmcn{1}$ \\ $\pmast54\pmcdot01$. & $\pmcn{0}$ \\ $\pmast54\pmcdot02$. & $\pmcn{2}$ \\ $\pmast55\pmcdot01$. & $\pmoc{x}{y}$ \\ $\pmast55\pmcdot02$. & $\pmoc{\pmdscf{R}{x}}{y}$ \\ $\pmast56\pmcdot01$. & $\pmdn{2}$ \\ $\pmast56\pmcdot02$. & $\pmorn{2}$ \end{tabular} \begin{tabular}{l l} $\pmast56\pmcdot03$. & $\pmorn{0}$ \\ $\pmast60\pmcdot01$. & $\pmsCl$ \\ $\pmast60\pmcdot02$. & $\pmsCle$ \\ $\pmast60\pmcdot03$. & $\pmClsn{2}$ \\ $\pmast60\pmcdot04$. & $\pmClsn{3}$ \\ $\pmast61\pmcdot01$. & $\pmsRl$ \\ $\pmast61\pmcdot02$. & $\pmsRle$ \\ $\pmast61\pmcdot03$. & $\pmReln{2}$ \\ $\pmast61\pmcdot04$. & $\pmReln{3}$ \\ $\pmast62\pmcdot01$. & $\pmrin$ \\ $\pmast63\pmcdot01$. & $\pmrt{x}$ \\ $\pmast63\pmcdot011$. & $\pmrti{1}{x}$ \\ $\pmast63\pmcdot02$. & $\pmrtc{0}{\alpha}$ \\ $\pmast63\pmcdot03$. & $\pmrtc{1}{\kappa}$ \\ $\pmast63\pmcdot04$. & $\pmrti{2}{\kappa}$ \\ $\pmast63\pmcdot041$. & $\pmrti{3}{\kappa}$ \\ $\pmast63\pmcdot05$. & $\pmrtc{2}{\kappa}$ \\ $\pmast63\pmcdot051$. & $\pmrtc{3}{\kappa}$ \\ $\pmast64\pmcdot01$. & $\pmrtrc{00}{\alpha}$ \\ $\pmast64\pmcdot011$. & $\pmrtri{11}{x}$ \\ $\pmast64\pmcdot012$. & $\pmrti{12}{x}$ \\ $\pmast64\pmcdot013$. & $\pmrti{21}{x}$ \\ $\pmast64\pmcdot014$. & $\pmrti{22}{x}$ \\ $\pmast64\pmcdot02$. & $\pmrtc{01}{\alpha}$ \\ $\pmast64\pmcdot021$. & $\pmrtc{10}{\alpha}$ \\ $\pmast64\pmcdot022$. & $\pmrtc{11}{\alpha}$ \\ $\pmast64\pmcdot03$. & $\pmrtrci{0}{1}{\alpha}$ \\ $\pmast64\pmcdot031$. & $\pmrtrci{1}{1}{\alpha}$ \\ $\pmast64\pmcdot04$. & $\pmrtric{1}{0}{\alpha}$ \\ $\pmast64\pmcdot041$. & $\pmrtric{1}{1}{\alpha}$ \\ $\pmast65\pmcdot01$. & $\pmrtdi{\alpha}{x}$ \\ $\pmast65\pmcdot02$. & $\pmrtdc{\alpha}{x}$ \end{tabular} \begin{tabular}{l l} $\pmast65\pmcdot03$. & $\pmrtdri{R}{x}$ \\ $\pmast65\pmcdot04$. & $\pmrtdrc{R}{x}$ \\ $\pmast65\pmcdot1$. & $\pmrtdri{R}{(x,y)}$ \\ $\pmast65\pmcdot11$. & $\pmrtdrc{R}{x_y}$\\ $\pmast65\pmcdot12$. & $\pmrtdrc{R}{x, y}$ \\ $\pmast70\pmcdot01$. & $\pmrdc{\alpha}{\beta}$ \\ $\pmast73\pmcdot01$. & $\alpha \pmsmbar \beta$ \\ $\pmast73\pmcdot02$. & $\pmsm$\\ $\pmast80\pmcdot01$. & $\pmSelp$ \\ $\pmast84\pmcdot01$. & $\pmexc$ \\ $\pmast84\pmcdot02$. & $\pmexcc{\gamma}$ \\ $\pmast84\pmcdot03$. & $\pmexcn$\\ $\pmast85\pmcdot5$. & $\pmselc{P}{\,y}$ \\ $\pmast88\pmcdot01$. & $\pmmultr$ \\ $\pmast88\pmcdot02$. & $\pmmultc$ \\ $\pmast88\pmcdot03$. & $\pmmultax$ \\ $\pmast90\pmcdot01$. & $\pmanc{R}$ \\ $\pmast90\pmcdot02$. & $\pmancc{R}$ \\ $\pmast91\pmcdot01$. & $\pmrst{R}$ \\ $\pmast91\pmcdot02$. & $\pmrts{R}$ \\ $\pmast91\pmcdot03$. & $\pmpot{R}$ \\ $\pmast91\pmcdot04$. & $\pmpotid{R}$ \\ $\pmast91\pmcdot05$. & $\pmpo{R}$ \\ $\pmast93\pmcdot01$. & $\pmB$ \\ $\pmast93\pmcdot02$. & $\pmmin{P}$ \\ $\pmast93\pmcdot021$. & $\pmmax{P}$ \\ $\pmast93\pmcdot03$. & $\pmgen{P}$ \\ $\pmast95\pmcdot01$. & $\pmefr{P}{Q}$ \hspace{.3cm} Dft [$\pmast95$] \\ $\pmast96\pmcdot01$. & $\pmipr{R}{x}$ \hspace{.415cm} Dft [$\pmast96$] \\ $\pmast96\pmcdot02$. & $\pmjpr{R}{x}$ \hspace{.375cm} Dft [$\pmast96$] \\ $\pmast97\pmcdot01$. & $\pmfr{R}{x}$ \\ $\pmast100\pmcdot01$. & $\pmNc$ \end{tabular} \onehalfspacing \begin{tabular}{l l} $\pmast100\pmcdot02$. & $\pmNC$ \\ $\pmast102\pmcdot01$. & $\pmNCat{\beta}{\alpha}$ \\ $\pmast103\pmcdot01$. & $\pmnoc{\alpha}$ \\ $\pmast103\pmcdot02$. & $\pmNoC$ \\ $\pmast104\pmcdot01$. & $\pmnca{1}{\alpha}$ \\ $\pmast104\pmcdot011$. & $\pmnca{2}{\alpha}$ \\ $\pmast104\pmcdot02$. & $\pmNca{1}$ \\ $\pmast104\pmcdot021$. & $\pmNca{2}$ \\ $\pmast104\pmcdot03$. & $\pmch{\mu}{1}$ \\ $\pmast104\pmcdot031$. & $\pmch{\mu}{2}$ \\ $\pmast105\pmcdot01$. & $\pmncd{1}{\alpha}$ \\ $\pmast105\pmcdot011$. & $\pmncd{2}{\alpha}$ \\ $\pmast105\pmcdot02$. & $\pmNcd{1}$ \\ $\pmast105\pmcdot021$. & $\pmNcd{2}$ \\ $\pmast105\pmcdot03$. & $\pmcl{\mu}{1}$ \\ $\pmast105\pmcdot031$. & $\pmcl{\mu}{2}$ \\ $\pmast106\pmcdot01$. & $\pmncll{0}{0}{\alpha}$ \\ $\pmast106\pmcdot011$. & $\pmnchh{1}{1}{\alpha}$ \\ $\pmast106\pmcdot012$. & $\pmncll{0}{1}{\alpha}$ \\ $\pmast106\pmcdot02$. & $\pmncaa{0}{1}{\alpha}$ \\ $\pmast106\pmcdot021$. & $\pmncdd{1}{0}{\alpha}$ \\ $\pmast106\pmcdot03$. & $\pmNCll{0}{0}$ \\ $\pmast106\pmcdot04$. & $\pmcll{\mu}{0}{0}$ \\ $\pmast106\pmcdot041$. & $\pmchh{\mu}{1}{1}$ \\ $\pmast110\pmcdot01$. & $\alpha \pmarsumc \beta$ \\ $\pmast110\pmcdot02$. & $\mu \pmarsumnc \nu$ \\ $\pmast110\pmcdot03$. & $\pmnc{\alpha} \pmarsumnc \mu$ \\ $\pmast110\pmcdot04$. & $\mu \pmarsumnc \pmnc{\alpha}$ \\ $\pmast110\pmcdot0561$. & $\mu \pmarsumnc \nu \pmarsumnc \varpi$ \\ $\pmast111\pmcdot01$. & $\kappa \pmsmsmb \lambda$ \\ $\pmast111\pmcdot02$. & $\pmcrp{S}{\beta}$ \\ $\pmast111\pmcdot03$. & $\pmsmsm$ \end{tabular} \begin{tabular}{l l} $\pmast112\pmcdot01$. & $\pmarsumcc{\kappa}$ \\ $\pmast112\pmcdot02$. & $\pmarsumcnc{\kappa}$ \\ $\pmast113\pmcdot02$. & $\beta \pmarprodc \alpha$ \\ $\pmast113\pmcdot03$. & $\mu \pmarprodnc \nu$ \\ $\pmast113\pmcdot04$. & $\pmnc{\beta} \pmarprodnc \mu$ \\ $\pmast113\pmcdot05$. & $\mu \pmarprodnc \pmnc{\alpha}$ \\ $\pmast113\pmcdot511$. & $\alpha \pmarprodc \beta \pmarprodc \gamma$ \\ $\pmast113\pmcdot541$. & $\mu \pmarprodnc \nu \pmarprodnc \varpi$ \\ $\pmast114\pmcdot01$. & $\pmarprodcnc{\kappa}$ \\ $\pmast115\pmcdot01$. & $\pmarprodcc{\kappa}$ \\ $\pmast115\pmcdot02$. & $\pmarcls$ \\ $\pmast116\pmcdot01$. & $\pmarexp{\alpha}{\beta}$ \\ $\pmast116\pmcdot02$. & $\pmarncexp{\mu}{\nu}$ \\ $\pmast116\pmcdot03$. & $\pmarncexp{(\pmnc{\alpha})}{\nu}$ \\ $\pmast116\pmcdot04$. & $\pmarncexp{\mu}{\pmnc{\beta}}$ \\ $\pmast117\pmcdot01$. & $\mu \pmarg \nu$ \\ $\pmast117\pmcdot02$. & $\mu \pmarg \pmnc{\alpha}$ \\ $\pmast117\pmcdot03$. & $\pmnc{\alpha} \pmarg \nu$ \\ $\pmast117\pmcdot04$. & $\mu \pmarl \nu$ \\ $\pmast117\pmcdot05$. & $\mu \pmargeq \nu$ \\ $\pmast117\pmcdot06$. & $\mu \pmarleq \nu$ \\ $\pmast119\pmcdot01$. & $\pmarsubt{\gamma}{\nu}$ \\ $\pmast119\pmcdot02$. & $\pmarsubt{\pmnc{\alpha}}{\nu}$ \\ $\pmast119\pmcdot03$. & $\pmarsubt{\gamma}{\pmnc{\beta}}$ \\ $\pmast120\pmcdot01$. & $\pmNCinduct$ \\ $\pmast120\pmcdot011$. & $\pmncinduct{\xi}$ \\ $\pmast120\pmcdot02$. & $\pmClsinduct$ \\ $\pmast120\pmcdot021$. & $\pmclsinduct{\xi}$ \\ $\pmast120\pmcdot03$. & $\pmInfinax$ \\ $\pmast120\pmcdot04$. & $\pminfinax{x}$ \\ $\pmast120\pmcdot43$. & $\pmspec{\beta}$ \\ $\pmast121\pmcdot01$. & $\pmintoo{x}{y}$ \end{tabular} \begin{tabular}{l l} $\pmast121\pmcdot011$. & $\pmintoc{x}{y}$ \\ $\pmast121\pmcdot012$. & $\pmintco{x}{y}$ \\ $\pmast121\pmcdot013$. & $\pmintcc{x}{y}$ \\ $\pmast121\pmcdot02$. & $\pmintnc{\nu}$ \\ $\pmast121\pmcdot03$. & $\pmfinid{P}$ \\ $\pmast121\pmcdot031$. & $\pmfin{P}$ \\ $\pmast121\pmcdot04$. & $\pmintt{\nu}{P}$ \\ $\pmast122\pmcdot01$. & $\pmprog$ \\ $\pmast123\pmcdot01$. & $\pmalephn{0}$ \\ $\pmast123\pmcdot02$. & $\pmsucc$ Dft [$\pmast123\textbf{---}4$] \\ $\pmast124\pmcdot01$. & $\pmclsrefl$ \\ $\pmast124\pmcdot02$. & $\pmncrefl$ \\ $\pmast124\pmcdot021$. & $\pmnc{\rho}\pmcin \pmncrefl$ \\ $\pmast124\pmcdot03$. & $\pmncmult$ \\ $\pmast126\pmcdot01$. & $\pmncind$ \\ $\pmast150\pmcdot01$. & $\pmrnsm{S}{Q}$ \\ $\pmast150\pmcdot02$. & $\pmrnsmd{S}{Q}$ \\ $\pmast150\pmcdot03$. & $\pmopsc{Q}{y}$ \\ $\pmast150\pmcdot04$. & $\pmdscf{R}{\pmrnsm{S}{Q}}$ \\ $\pmast150\pmcdot05$. & $\pmrnsm{R}{\pmrnsm{S}{Q}}$ \\ $\pmast151\pmcdot01$. & $\pmsmorb{P}{Q}$ \\ $\pmast151\pmcdot02$. & $\pmSmor$ \\ $\pmast152\pmcdot01$. & $\pmNr$ \\ $\pmast152\pmcdot02$. & $\pmNR$ \\ $\pmast153\pmcdot01$. & $\pmsrrn{1}$ \\ $\pmast154\pmcdot01$. & $\pmNRat{\gamma}{X}$ \\ $\pmast155\pmcdot01$. & $\pmnor{P}$ \\ $\pmast155\pmcdot02$. & $\pmNoR$ \\ $\pmast160\pmcdot01$. & $\pmrsum{P}{Q}$ \\ $\pmast161\pmcdot01$. & $\pmrsumb{P}{x}$ \\ $\pmast161\pmcdot02$. & $\pmrsume{x}{P}$ \\ $\pmast161\pmcdot212$. & $\pmrsumb{P}{\pmrsumb{x}{y}}$ \end{tabular} \begin{tabular}{l l} $\pmast161\pmcdot213$. & $\pmrsume{\pmrsume{x}{y}}{P}$ \\ $\pmast162\pmcdot01$. & $\pmrsumr{P}$ \\ $\pmast163\pmcdot01$. & $\pmrsumrex{2}$ \\ $\pmast164\pmcdot01$. & $\pmsmorsmorb{P}{Q}$ \\ $\pmast164\pmcdot02$. & $\pmSmorsmor$ \\ $\pmast166\pmcdot01$. & $\pmrprod{Q}{P}$ \\ $\pmast166\pmcdot421$. & $\pmrprod{P}{\pmrprod{Q}{R}}$ \\ $\pmast170\pmcdot01$. & $\pmRfdcl{P}$ \\ $\pmast170\pmcdot02$. & $\pmRfdlc{P}$ \\ $\pmast171\pmcdot01$. & $\pmRfddf{P}$ \\ $\pmast171\pmcdot02$. & $\pmRfdfd{P}$ \\ $\pmast172\pmcdot01$. & $\pmrfprod{P}$ \\ $\pmast173\pmcdot01$. & $\pmRfprod{P}$ \\ $\pmast174\pmcdot01$. & $\pmrarrel{3}$ \\ $\pmast176\pmcdot01$. & $P \pmrexp Q$ \\ $\pmast176\pmcdot02$. & $\pmRexp{P}{Q}$ \\ $\pmast180\pmcdot01$. & $\pmrnsum{P}{Q}$ \\ $\pmast180\pmcdot02$. & $\pmrndsum{\mu}{\nu}$ \\ $\pmast180\pmcdot03$. & $\pmrndsum{\pmnr{P}}{\nu}$ \\ $\pmast180\pmcdot04$. & $\pmrndsum{\mu}{\pmnr{Q}}$ \\ $\pmast180\pmcdot561$. & $\pmrndsum{\mu}{\pmrndsum{\nu}{\varpi}}$ \\ $\pmast181\pmcdot01$. & $\pmrnsumru{P}{x}$ \\ $\pmast181\pmcdot011$. & $\pmrnsumur{x}{P}$ \\ $\pmast181\pmcdot02$. & $\pmrndsum{\mu}{\pmrn{1}}$ \\ $\pmast181\pmcdot021$. & $\pmrndsum{\pmrn{1}}{\mu}$ \\ $\pmast181\pmcdot03$. & $\pmrndsum{\pmnr{P}}{\pmrn{1}}$ \\ $\pmast181\pmcdot031$. & $\pmrndsum{\pmrn{1}}{\pmnr{P}}$ \\ $\pmast181\pmcdot04$. & $\pmrndsum{\pmrn{1}}{\pmrn{1}}$ \\ $\pmast181\pmcdot561$. & $\pmrndsum{\mu}{\pmrndsum{\pmrn{1}}{\pmrn{1}}}$ \\ $\pmast181\pmcdot571$. & $\pmrndsum{\pmrn{1}}{\pmrndsum{\pmrn{1}}{\mu}}$ \\ $\pmast182\pmcdot01$. & $\pmrsep{\pmop}$ \\ $\pmast183\pmcdot01$. & $\pmrnsumf{P}$ \end{tabular} \begin{tabular}{l l} $\pmast184\pmcdot01$. & $\pmrnprod{\mu}{\nu}$ \\ $\pmast184\pmcdot02$. & $\pmrnprod{\pmnr{P}}{\nu}$ \\ $\pmast184\pmcdot03$. & $\pmrnprod{\mu}{\pmnr{Q}}$ \\ $\pmast184\pmcdot32$. & $\pmrnprod{\mu}{\pmrnprod{\nu}{\varpi}}$ \\ $\pmast185\pmcdot01$. & $\pmrnprodf{P}$ \\ $\pmast186\pmcdot01$. & $\pmrnexp{r}{\mu}{\nu}$ \\ $\pmast186\pmcdot02$. & $\pmrnexp{r}{(\pmnr{P})}{\nu}$ \\ $\pmast186\pmcdot03$. & $\pmrnexp{r}{\mu}{(\pmnr{Q})}$ \\ $\pmast201\pmcdot01$. & $\pmtrans$ \\ $\pmast202\pmcdot01$. & $\pmconnex$ \\ $\pmast204\pmcdot01$. & $\pmser$ \\ $\pmast206\pmcdot01$. & $\pmSeq{P}$ \\ $\pmast206\pmcdot02$. & $\pmPrec{P}$ \\ $\pmast207\pmcdot01$. & $\pmlt{P}$ \\ $\pmast207\pmcdot02$. & $\pmtl{P}$ \\ $\pmast207\pmcdot03$. & $\pmLimax{P}$ \\ $\pmast207\pmcdot04$. & $\pmLimin{P}$ \\ $\pmast208\pmcdot01$. & $\pmcror{P}$ \\ $\pmast211\pmcdot01$. & $\pmsect{P}$ \\ $\pmast212\pmcdot01$. & $\pmseg{P}$ \\ $\pmast212\pmcdot02$. & $\pmsym{P}$ \\ $\pmast213\pmcdot01$. & $\pmsectr{P}$ \\ $\pmast214\pmcdot01$. & $\pmded$ \\ $\pmast214\pmcdot02$. & $\pmsded$ \\ $\pmast215\pmcdot01$. & $\pmstr{P}$ \\ $\pmast216\pmcdot01$. & $\pmDer{P}$ \\ $\pmast216\pmcdot02$. & $\pmden{P}$ \\ $\pmast216\pmcdot03$. & $\pmclsd{P}$ \\ $\pmast216\pmcdot04$. & $\pmperf{P}$ \\ $\pmast216\pmcdot05$. & $\pmders{P}$ \\ $\pmast230\pmcdot01$. & $\pmconv{R}{Q}{\alpha}$ \\ $\pmast230\pmcdot02$. & $\pmConv{Q}$ \end{tabular} \begin{tabular}{l l} $\pmast231\pmcdot01$. & $\pmlsc{P}{R}{Q}$ \\ $\pmast231\pmcdot02$. & $\pmosc{P}{R}{Q}$ \\ $\pmast232\pmcdot01$. & $\pmlscl{P}{R}{Q}{\alpha}$ \\ $\pmast232\pmcdot02$. & $\pmoscl{P}{R}{Q}{\alpha}$ \\ $\pmast233\pmcdot01$. & $\pmLmx{P}{R}{Q}$ \\ $\pmast233\pmcdot02$. & $\pmLimf{R}{P}{Q}$ \\ $\pmast234\pmcdot01$. & $\pmscf{P}{Q}{R}$ \\ $\pmast234\pmcdot02$. & $\pmosf{P}{Q}{R}$ \\ $\pmast234\pmcdot03$. & $\pmctf{P}{Q}{R}$ \\ $\pmast234\pmcdot04$. & $\pmcontinf{P}{Q}{R}$ \\ $\pmast234\pmcdot05$. & $\pmcontin{P}{Q}$ \\ $\pmast250\pmcdot01$. & $\pmbord$ \\ $\pmast250\pmcdot02$. & $\pmword$ \\ $\pmast251\pmcdot01$. & $\pmordn$ \\ $\pmast254\pmcdot01$. & $\pmLess$ \\ $\pmast254\pmcdot02$. & $\pmPsc$ \\ $\pmast255\pmcdot01$. & $\pmorle$ \\ $\pmast255\pmcdot02$. & $\pmorgr$ \\ $\pmast255\pmcdot03$. & $\pmnoo$ \\ $\pmast255\pmcdot04$. & $\pmorleq$ \\ $\pmast255\pmcdot05$. & $\pmorgrq$ \\ $\pmast255\pmcdot06$. & $\mu \pmorle \pmnr{P}$ \\ $\pmast255\pmcdot07$. & $\pmnr{P} \pmorle \mu$ \\ $\pmast256\pmcdot01$. & $\pmm$ \hspace{2ex} Dft [\(\pmast256\)] \\ $\pmast256\pmcdot02$. & $\pmn \,$ \hspace{2ex} Dft [\(\pmast256\)] \\ $\pmast257\pmcdot01$. & $\pmtranc{R}{Q}{x}$ \\ $\pmast257\pmcdot02$. & $\pmtrpot{Q}{R}{x}$ \\ $\pmast259\pmcdot01$. & $\pma$ \hspace{2.75ex} Dft [\(\pmast256\)] \\ $\pmast259\pmcdot02$. & $\pmaw$ \hspace{1.2ex} Dft [\(\pmast256\)] \\ $\pmast259\pmcdot03$. & $\pmwa$ \\ $\pmast260\pmcdot01$. & $\pmintf$ \\ $\pmast261\pmcdot01$. & $\pmserinf$ \end{tabular} \begin{tabular}{l l} $\pmast261\pmcdot02$. & $\pmwordinf$ \\ $\pmast261\pmcdot03$. & $\pmserfin$ \\ $\pmast261\pmcdot04$. & $\pmwordfin$ \\ $\pmast261\pmcdot05$. & $\pmwordind$ \\ $\pmast262\pmcdot01$. & $\pmordnfin$ \\ $\pmast262\pmcdot02$. & $\pmordninf$ \\ $\pmast262\pmcdot03$. & $\pmfinord{\mu}$ \\ $\pmast263\pmcdot01$. & $\pmom$ \\ $\pmast263\pmcdot02$. & $\pmn$ \hspace{3.4ex} Dft [\(\pmast263\)] \\ $\pmast264\pmcdot01$. & $\pmpr{P}$ \hspace{2ex} Dft [\(\pmast263\)] \\ $\pmast264\pmcdot429$. & $\pmrnprod{\pmrn{1}}{\alpha}$ \\ $\pmast265\pmcdot01$. & $\pmomn{1}$ \\ $\pmast265\pmcdot02$. & $\pmalephn{1}$ \\ $\pmast265\pmcdot03$. & $\pmomn{2}$ \\ $\pmast265\pmcdot04$. & $\pmalephn{2}$ \\ $\pmast265\pmcdot05$. & $\pmm$ \hspace{3.2ex} Dft [\(\pmast265\)] \\ $\pmast265\pmcdot06$. & $\pmn$ \hspace{3.5ex} Dft [\(\pmast265\)] \\ $\pmast270\pmcdot01$. & $\pmComp$ \\ $\pmast271\pmcdot01$. & $\pmmed$ \\ $\pmast272\pmcdot01$. & $\pmsimp{T}{P}{Q}$ \\ $\pmast273\pmcdot01$. & $\pmrats$ \\ $\pmast273\pmcdot02$. & $\pmsimps{R}{SPQ}{T}$ \hspace{3.4ex} Dft [\(\pmast273\)] \\ $\pmast273\pmcdot03$. & $\pmSimp{R}{S}{PQ}$ \hspace{3.5ex} Dft [\(\pmast273\)] \\ $\pmast273\pmcdot04$. & $\pmSimps{T}{RSPQ}$ \hspace{4.9ex} Dft [\(\pmast273\)] \\ $\pmast274\pmcdot01$. & $\pmsfcls{P}$ \\ $\pmast274\pmcdot02$. & $\pmsfclsm{P}{\kappa}$ \hspace{3.4ex} Dft [\(\pmast274\)] \\ $\pmast274\pmcdot03$. & $\pmsfclsp{T}{\kappa}$ \hspace{3.7ex} Dft [\(\pmast274\)] \\ $\pmast274\pmcdot04$. & $\pmsfclsmp{\kappa}$ \hspace{3ex} Dft [\(\pmast274\)] \\ $\pmast275\pmcdot01$. & $\pmcser$ \\ $\pmast276\pmcdot01$. & $\pmcsercl{P}$ \\ $\pmast276\pmcdot02$. & $\pma$ \hspace{7.3ex} Dft [\(\pmast276\)] \\ $\pmast276\pmcdot03$. & $\pmsfclsm{P}{\lambda}$ \hspace{4ex} Dft [\(\pmast276\)] \end{tabular} \begin{tabular}{l l} $\pmast276\pmcdot04$. & $\pmcsercls{T}{P}$ \hspace{8.2ex} Dft [\(\pmast276\)] \\ $\pmast276\pmcdot05$. & $\pmCsercls{P}{\kappa}$ \hspace{6.25ex} Dft [\(\pmast276\)] \\ $\pmast300\pmcdot01$. & $\pmu$ \\ $\pmast300\pmcdot02$. & $\pmrnum$ \\ $\pmast300\pmcdot03$. & $\pmrnumid$ \\ $\pmast301\pmcdot01$. & $R_p$ \hspace{8.2ex} Dft [\(\pmast301\)] \\ $\pmast301\pmcdot02$. & $\text{num}(R)$ \hspace{3ex} Dft [\(\pmast301\)] \\ $\pmast301\pmcdot03$. & $\pmrpwr{R}{\sigma}$ \\ $\pmast302\pmcdot01$. & $\pmPrm$ \\ $\pmast302\pmcdot02$. & $\pmrprm{\rho}{\sigma}{\mu}{\nu}$ \\ $\pmast302\pmcdot03$. & $\pmprm{\rho}{\sigma}{\mu}{\nu}$ \\ $\pmast302\pmcdot04$. & $\pmhcf{\mu}{\nu}$ \\ $\pmast302\pmcdot05$. & $\pmlcm{\mu}{\nu}$ \\ $\pmast303\pmcdot01$. & $\pmrat{\mu}{\nu}$ \\ $\pmast303\pmcdot02$. & $\pmqn{0}$ \\ $\pmast303\pmcdot03$. & $\pmqnil$ \\ $\pmast303\pmcdot04$. & $\pmRat$ \\ $\pmast303\pmcdot05$. & $\pmRatdef$ \\ $\pmast304\pmcdot01$. & $\pmqnle{X}{Y}$ \\ $\pmast304\pmcdot02$. & $\pmqnLe$ \\ $\pmast304\pmcdot03$. & $\pmqnlez$ \\ $\pmast305\pmcdot01$. & $\pmprodsr{X}{Y}$ \\ $\pmast306\pmcdot01$. & $\pmsumsr{X}{Y}$ \\ $\pmast307\pmcdot01$. & $\pmratn$ \\ $\pmast307\pmcdot011$. & $\pmratg$ \\ $\pmast307\pmcdot02$. & $\pmRatnle$ \\ $\pmast307\pmcdot021$. & $\pmRatngr$ \\ $\pmast307\pmcdot03$. & $\pmRatgle$ \\ $\pmast307\pmcdot031$. & $\pmRatggr$ \\ $\pmast307\pmcdot04$. & $\pmratnLe$ \\ $\pmast307\pmcdot05$. & $\pmratgLe$ \\ $\pmast308\pmcdot01$. & $\pmratssub{X}{Y}$ \end{tabular} \begin{tabular}{l l} $\pmast308\pmcdot02$. & $\pmsumgr{X}{Y}$ \\ $\pmast309\pmcdot01$. & $\pmprodgr{X}{Y}$ \\ $\pmast310\pmcdot01$. & $\pmrenp$ \\ $\pmast310\pmcdot011$. & $\pmrenpz$ \\ $\pmast310\pmcdot02$. & $\pmrenn$ \\ $\pmast310\pmcdot021$. & $\pmrennz$ \\ $\pmast310\pmcdot03$. & $\pmreng$ \\ $\pmast311\pmcdot01$. & $\pmconc{\mu,\nu,...}$ \\ $\pmast311\pmcdot02$. & $\pmrensumc{\mu}{\nu}$ \\ $\pmast312\pmcdot01$. & $\pmrensub{\mu}{\nu}$ \\ $\pmast312\pmcdot02$. & $\pmrensuma{\mu}{\nu}$ \\ $\pmast313\pmcdot01$. & $\pmrenproda{\mu}{\nu}$ \\ $\pmast314\pmcdot01$. & $\pmrenrsum{X}{Y}$ \\ $\pmast314\pmcdot02$. & $\pmrenrprod{X}{Y}$ \\ $\pmast314\pmcdot03$. & $\pmrenr$ \\ $\pmast314\pmcdot04$. & $\pmrenrssum{M}{N}$ \\ $\pmast314\pmcdot05$. & $\pmrenrsprod{M}{N}$ \\ $\pmast330\pmcdot01$. & $\pmcr{\alpha}$ \\ $\pmast330\pmcdot02$. & $\pmabel$ \\ $\pmast330\pmcdot03$. & $\pmvfm{\alpha}$ \\ $\pmast330\pmcdot04$. & $\pmvfmcl$ \\ $\pmast330\pmcdot05$. & $\pmvffb{\kappa}$ \\ $\pmast331\pmcdot01$. & $\pmconx{\kappa}$ \\ $\pmast331\pmcdot02$. & $\pmconxfm$ \\ $\pmast332\pmcdot01$. & $\pmfrep{\kappa}{P}$ \\ $\pmast333\pmcdot01$. & $\pmfopen{\kappa}$ \\ $\pmast333\pmcdot011$. & $\pmfopennid{\kappa}$ \\ $\pmast333\pmcdot02$. & $\pmfmap$ \\ $\pmast333\pmcdot03$. & $\pmfmapconx$ \end{tabular} \begin{tabular}{l l} $\pmast334\pmcdot01$. & $\pmtrsp{\kappa}$ \\ $\pmast334\pmcdot02$. & $\pmfmtrs$ \\ $\pmast334\pmcdot03$. & $\pmfmconnex$ \\ $\pmast334\pmcdot04$. & $\pmfmsr$ \\ $\pmast334\pmcdot05$. & $\pmfmasym$ \\ $\pmast335\pmcdot01$. & $\pminit{\kappa}$ \\ $\pmast335\pmcdot02$. & $\pmfminit$ \\ $\pmast336\pmcdot01$. & $\pmvr{\kappa}$ \\ $\pmast336\pmcdot011$. & $\pmvrnid{\kappa}$ \\ $\pmast336\pmcdot02$. & $\pmarvs{a}$ \\ $\pmast351\pmcdot01$. & $\pmfmsubm$ \\ $\pmast352\pmcdot01$. & $\pmvrm{T}{\kappa}$ \\ $\pmast352\pmcdot02$. & $\pmvrmg{T}{\kappa}$ \\ $\pmast353\pmcdot01$. & $\pmfmrt$ \\ $\pmast353\pmcdot02$. & $\pmfmcx$ \\ $\pmast353\pmcdot03$. & $\pmfmrtcx$ \\ $\pmast354\pmcdot01$. & $\pmfmg{\kappa}$ \\ $\pmast354\pmcdot02$. & $\pmrtnet{a}{\lambda}$ \\ $\pmast354\pmcdot03$. & $\pmfmgrp$ \\ $\pmast356\pmcdot01$. & $\pmrems{X}{\kappa}$ \\ $\pmast370\pmcdot01$. & $\pmfmcycl$ \\ $\pmast370\pmcdot02$. & $\pmcycl{K}{\kappa}$ \\ $\pmast370\pmcdot03$. & $\pmcycli{I}{\kappa}$ \\ $\pmast371\pmcdot01$. & $\pmvser{W}{\kappa}$ \\ $\pmast372\pmcdot01$. & $\pmintsecvser{\nu}{\kappa}$ \\ $\pmast373\pmcdot01$. & $\pmsfmid{M}{\nu}{\kappa}$ \hspace{2ex} Dft [\(\pmast373\text{---}5\)]\\ $\pmast373\pmcdot02$. & $\pmprime$ \\ $\pmast373\pmcdot03$. & $\pmsmltid{S}{\nu}$ \hspace{0.75ex} Dft [\(\pmast373\text{---}5\)]\\ $\pmast375\pmcdot01$. & $\pmprrt{\mu}{\nu}{\kappa}$ \end{tabular} \end{document}