diff --git a/ibis/backends/base/__init__.py b/ibis/backends/base/__init__.py
index bbff70e5f32a..faa0e6dc963c 100644
--- a/ibis/backends/base/__init__.py
+++ b/ibis/backends/base/__init__.py
@@ -465,6 +465,9 @@ def __getstate__(self):
             _con_kwargs=self._con_kwargs,
         )
 
+    def __rich_repr__(self):
+        yield "name", self.name
+
     def __hash__(self):
         return hash(self.db_identity)
 
diff --git a/ibis/common/collections.py b/ibis/common/collections.py
new file mode 100644
index 000000000000..ca673f152bf4
--- /dev/null
+++ b/ibis/common/collections.py
@@ -0,0 +1,73 @@
+from __future__ import annotations
+
+from collections.abc import Mapping
+
+from typing_extensions import Self
+
+
+class MapSet(Mapping):
+    def _check_conflict(self, other):
+        common_keys = self.keys() & other.keys()
+        for key in common_keys:
+            left, right = self[key], other[key]
+            if left != right:
+                raise ValueError(
+                    f"Conflicting values for key `{key}`: {left} != {right}"
+                )
+        return common_keys
+
+    def __ge__(self, other: Self) -> bool:
+        if not isinstance(other, self.__class__):
+            return NotImplemented
+        common_keys = self._check_conflict(other)
+        return other.keys() == common_keys
+
+    def __gt__(self, other: Self) -> bool:
+        if not isinstance(other, self.__class__):
+            return NotImplemented
+        return len(self) > len(other) and self.__ge__(other)
+
+    def __le__(self, other: Self) -> bool:
+        if not isinstance(other, self.__class__):
+            return NotImplemented
+        common_keys = self._check_conflict(other)
+        return self.keys() == common_keys
+
+    def __lt__(self, other: Self) -> bool:
+        if not isinstance(other, self.__class__):
+            return NotImplemented
+        return len(self) < len(other) and self.__le__(other)
+
+    def __and__(self, other: Self) -> Self:
+        if not isinstance(other, self.__class__):
+            return NotImplemented
+        common_keys = self._check_conflict(other)
+        intersection = {k: v for k, v in self.items() if k in common_keys}
+        return self.__class__(intersection)
+
+    def __sub__(self, other: Self) -> Self:
+        if not isinstance(other, self.__class__):
+            return NotImplemented
+        common_keys = self._check_conflict(other)
+        difference = {k: v for k, v in self.items() if k not in common_keys}
+        return self.__class__(difference)
+
+    def __or__(self, other: Self) -> Self:
+        if not isinstance(other, self.__class__):
+            return NotImplemented
+        self._check_conflict(other)
+        union = {**self, **other}
+        return self.__class__(union)
+
+    def __xor__(self, other: Self) -> Self:
+        if not isinstance(other, self.__class__):
+            return NotImplemented
+        left = self - other
+        right = other - self
+        left._check_conflict(right)
+        union = {**left, **right}
+        return self.__class__(union)
+
+    def isdisjoint(self, other: Self) -> bool:
+        common_keys = self._check_conflict(other)
+        return not common_keys
diff --git a/ibis/common/tests/test_collections.py b/ibis/common/tests/test_collections.py
new file mode 100644
index 000000000000..f82716200745
--- /dev/null
+++ b/ibis/common/tests/test_collections.py
@@ -0,0 +1,130 @@
+from collections.abc import ItemsView, Iterator, KeysView, ValuesView
+
+import pytest
+
+from ibis.common.collections import MapSet
+
+
+class MySchema(MapSet):
+    def __init__(self, dct=None, **kwargs):
+        self._fields = dict(dct or kwargs)
+
+    def __repr__(self):
+        return f'{self.__class__.__name__}({self._fields})'
+
+    def __getitem__(self, key):
+        return self._fields[key]
+
+    def __iter__(self):
+        return iter(self._fields)
+
+    def __len__(self):
+        return len(self._fields)
+
+    def identical(self, other):
+        return type(self) == type(other) and tuple(self.items()) == tuple(other.items())
+
+
+def test_myschema_identical():
+    ms1 = MySchema(a=1, b=2)
+    ms2 = MySchema(a=1, b=2)
+    ms3 = MySchema(b=2, a=1)
+    ms4 = MySchema(a=1, b=2, c=3)
+    ms5 = {}
+
+    assert ms1.identical(ms2)
+    assert not ms1.identical(ms3)
+    assert not ms1.identical(ms4)
+    assert not ms1.identical(ms5)
+
+
+def test_mapset_mapping_api():
+    ms = MySchema(a=1, b=2)
+    assert ms['a'] == 1
+    assert ms['b'] == 2
+    assert len(ms) == 2
+    assert isinstance(iter(ms), Iterator)
+    assert list(ms) == ['a', 'b']
+    assert isinstance(ms.keys(), KeysView)
+    assert list(ms.keys()) == ['a', 'b']
+    assert isinstance(ms.values(), ValuesView)
+    assert list(ms.values()) == [1, 2]
+    assert isinstance(ms.items(), ItemsView)
+    assert list(ms.items()) == [('a', 1), ('b', 2)]
+    assert ms.get('a') == 1
+    assert ms.get('c') is None
+    assert ms.get('c', 3) == 3
+    assert 'a' in ms
+    assert 'c' not in ms
+    assert ms == ms
+    assert ms != MySchema(a=1, b=2, c=3)
+
+
+def test_mapset_set_api():
+    a = MySchema(a=1, b=2)
+    a_ = MySchema(a=1, b=-2)
+    b = MySchema(a=1, b=2, c=3)
+    b_ = MySchema(a=1, b=2, c=-3)
+    f = MySchema(d=4, e=5)
+
+    # disjoint
+    assert not a.isdisjoint(b)
+    assert a.isdisjoint(f)
+
+    # __eq__, __ne__
+    assert a == a
+    assert a != a_
+    assert b == b
+    assert b != b_
+
+    # __le__, __lt__
+    assert a < b
+    assert a <= b
+    assert a <= a
+    assert not b <= a
+    assert not b < a
+    with pytest.raises(ValueError, match="Conflicting values"):
+        # duplicate keys with different values
+        a <= a_  # noqa: B015
+
+    # __gt__, __ge__
+    assert b > a
+    assert b >= a
+    assert a >= a
+    assert not a >= b
+    assert not a > b
+    assert not a_ > a
+    with pytest.raises(ValueError, match="Conflicting values"):
+        a_ >= a  # noqa: B015
+
+    # __and__
+    with pytest.raises(ValueError, match="Conflicting values"):
+        a & a_
+    with pytest.raises(ValueError, match="Conflicting values"):
+        b & b_
+    assert (a & b).identical(a)
+    assert (a & f).identical(MySchema())
+
+    # __or__
+    assert (a | a).identical(a)
+    assert (a | b).identical(b)
+    assert (a | f).identical(MySchema(a=1, b=2, d=4, e=5))
+    with pytest.raises(ValueError, match="Conflicting values"):
+        a | a_
+
+    # __sub__
+    with pytest.raises(ValueError, match="Conflicting values"):
+        a - a_
+    assert (a - b).identical(MySchema())
+    assert (b - a).identical(MySchema(c=3))
+    assert (a - f).identical(a)
+    assert (f - a).identical(f)
+
+    # __xor__
+    with pytest.raises(ValueError, match="Conflicting values"):
+        a ^ a_
+
+    assert (a ^ b).identical(MySchema(c=3))
+    assert (b ^ a).identical(MySchema(c=3))
+    assert (a ^ f).identical(MySchema(a=1, b=2, d=4, e=5))
+    assert (f ^ a).identical(MySchema(d=4, e=5, a=1, b=2))
diff --git a/ibis/expr/datatypes/core.py b/ibis/expr/datatypes/core.py
index a5ad26c24901..cf7b11aee423 100644
--- a/ibis/expr/datatypes/core.py
+++ b/ibis/expr/datatypes/core.py
@@ -18,6 +18,7 @@
 
 import ibis.expr.types as ir
 from ibis.common.annotations import attribute, optional
+from ibis.common.collections import MapSet
 from ibis.common.grounds import Concrete, Singleton
 from ibis.common.validators import (
     all_of,
@@ -675,7 +676,7 @@ def _pretty_piece(self) -> str:
 
 
 @public
-class Struct(Parametric, Mapping):
+class Struct(Parametric, MapSet):
     """Structured values."""
 
     fields = frozendict_of(instance_of(str), datatype)
diff --git a/ibis/expr/datatypes/tests/test_core.py b/ibis/expr/datatypes/tests/test_core.py
index 93364dadb601..5e1340dfa6af 100644
--- a/ibis/expr/datatypes/tests/test_core.py
+++ b/ibis/expr/datatypes/tests/test_core.py
@@ -400,6 +400,37 @@ def test_struct_mapping_api():
         s['e'] = dt.int8
 
 
+def test_struct_set_operations():
+    a = dt.Struct({'a': dt.string, 'b': dt.int64, 'c': dt.float64})
+    b = dt.Struct({'a': dt.string, 'c': dt.float64, 'd': dt.boolean, 'e': dt.date})
+    c = dt.Struct({'i': dt.int64, 'j': dt.float64, 'k': dt.string})
+    d = dt.Struct({'i': dt.int64, 'j': dt.float64, 'k': dt.string, 'l': dt.boolean})
+
+    assert a & b == dt.Struct({'a': dt.string, 'c': dt.float64})
+    assert a | b == dt.Struct(
+        {'a': dt.string, 'b': dt.int64, 'c': dt.float64, 'd': dt.boolean, 'e': dt.date}
+    )
+    assert a - b == dt.Struct({'b': dt.int64})
+    assert b - a == dt.Struct({'d': dt.boolean, 'e': dt.date})
+    assert a ^ b == dt.Struct({'b': dt.int64, 'd': dt.boolean, 'e': dt.date})
+
+    assert not a.isdisjoint(b)
+    assert a.isdisjoint(c)
+
+    assert a <= a
+    assert a >= a
+    assert not a < a
+    assert not a > a
+    assert not a <= b
+    assert not a >= b
+    assert not a >= c
+    assert not a <= c
+    assert c <= d
+    assert c < d
+    assert d >= c
+    assert d > c
+
+
 def test_singleton_null():
     assert dt.null is dt.Null()
 
diff --git a/ibis/expr/operations/core.py b/ibis/expr/operations/core.py
index ec12a6587c99..aaf3c1f598c6 100644
--- a/ibis/expr/operations/core.py
+++ b/ibis/expr/operations/core.py
@@ -35,6 +35,9 @@ def to_expr(self):
     # Avoid custom repr for performance reasons
     __repr__ = object.__repr__
 
+    def __rich_repr__(self):
+        return zip(self.__argnames__, self.__args__)
+
 
 @public
 class Named(ABC):
diff --git a/ibis/expr/operations/relations.py b/ibis/expr/operations/relations.py
index be9f1710537e..4bb003afd258 100644
--- a/ibis/expr/operations/relations.py
+++ b/ibis/expr/operations/relations.py
@@ -79,12 +79,6 @@ class InMemoryTable(PhysicalTable):
     def data(self) -> util.ToFrame:
         """Return the data of an in-memory table."""
 
-    def has_resolved_name(self):
-        return True
-
-    def resolve_name(self):
-        return self.name
-
 
 # TODO(kszucs): desperately need to clean this up, the majority of this
 # functionality should be handled by input rules for the Join class
@@ -176,8 +170,13 @@ def __init__(self, left, right, predicates, **kwargs):
 
     @property
     def schema(self):
-        # For joins retaining both table schemas, merge them together here
-        return self.left.schema.merge(self.right.schema)
+        # TODO(kszucs): use `return self.lefts.chema | self.right.schema` instead which
+        # eliminates unnecessary projection over the join, but currently breaks the
+        # pandas backend
+        left, right = self.left.schema, self.right.schema
+        if duplicates := left.keys() & right.keys():
+            raise com.IntegrityError(f'Duplicate column name(s): {duplicates}')
+        return sch.Schema({**left, **right})
 
 
 @public
diff --git a/ibis/expr/operations/window.py b/ibis/expr/operations/window.py
index 6071bfba2104..d75478a33de6 100644
--- a/ibis/expr/operations/window.py
+++ b/ibis/expr/operations/window.py
@@ -25,9 +25,6 @@ def following(self) -> bool:
         return not self.preceding
 
 
-# perhaps have separate window frames, RowsWindowFrame and RangeWindowFrame
-
-
 @public
 class WindowFrame(Value):
     """A window frame operation bound to a table."""
diff --git a/ibis/expr/schema.py b/ibis/expr/schema.py
index 4888dfecaf2e..9ce37fa52c98 100644
--- a/ibis/expr/schema.py
+++ b/ibis/expr/schema.py
@@ -7,10 +7,11 @@
 
 import ibis.expr.datatypes as dt
 from ibis.common.annotations import attribute
+from ibis.common.collections import MapSet
 from ibis.common.exceptions import IntegrityError
 from ibis.common.grounds import Concrete
 from ibis.common.validators import Coercible, frozendict_of, instance_of, validator
-from ibis.util import indent
+from ibis.util import deprecated, indent
 
 if TYPE_CHECKING:
     import pandas as pd
@@ -43,7 +44,7 @@ def datatype(arg, **kwargs):
     return dt.dtype(arg)
 
 
-class Schema(Concrete, Mapping, Coercible):
+class Schema(Concrete, Coercible, MapSet):
     """An object for holding table schema information."""
 
     fields = frozendict_of(instance_of(str), datatype)
@@ -61,6 +62,10 @@ def __repr__(self) -> str:
             )
         )
 
+    def __rich_repr__(self):
+        for name, dtype in self.items():
+            yield name, str(dtype)
+
     def __len__(self) -> int:
         return len(self.fields)
 
@@ -152,14 +157,7 @@ def to_pyarrow(self):
     def as_struct(self) -> dt.Struct:
         return dt.Struct(self)
 
-    def __gt__(self, other: Schema) -> bool:
-        """Return whether `self` is a strict superset of `other`."""
-        return set(self.items()) > set(other.items())
-
-    def __ge__(self, other: Schema) -> bool:
-        """Return whether `self` is a superset of or equal to `other`."""
-        return set(self.items()) >= set(other.items())
-
+    @deprecated(as_of="5.0", removed_in="6.0", instead="use union operator instead")
     def merge(self, other: Schema) -> Schema:
         """Merge `other` to `self`.
 
diff --git a/ibis/expr/tests/test_rules.py b/ibis/expr/tests/test_rules.py
index 9d27d94e2da2..12c336313a30 100644
--- a/ibis/expr/tests/test_rules.py
+++ b/ibis/expr/tests/test_rules.py
@@ -332,7 +332,7 @@ def test_table_with_schema(table):
 )
 def test_table_with_schema_invalid(table):
     validator = rlz.table(schema=[('group', dt.double), ('value', dt.timestamp)])
-    with pytest.raises(IbisTypeError):
+    with pytest.raises(ValueError):
         validator(table)
 
 
diff --git a/ibis/expr/tests/test_schema.py b/ibis/expr/tests/test_schema.py
index 77481e14c203..f4e65e9b376b 100644
--- a/ibis/expr/tests/test_schema.py
+++ b/ibis/expr/tests/test_schema.py
@@ -328,3 +328,34 @@ def test_schema_is_coercible():
 def test_schema_shorthand_supports_kwargs():
     s = sch.schema(a=dt.int64, b=dt.Array(dt.int64))
     assert s == sch.Schema({'a': dt.int64, 'b': dt.Array(dt.int64)})
+
+
+def test_schema_set_operations():
+    a = sch.Schema({'a': dt.string, 'b': dt.int64, 'c': dt.float64})
+    b = sch.Schema({'a': dt.string, 'c': dt.float64, 'd': dt.boolean, 'e': dt.date})
+    c = sch.Schema({'i': dt.int64, 'j': dt.float64, 'k': dt.string})
+    d = sch.Schema({'i': dt.int64, 'j': dt.float64, 'k': dt.string, 'l': dt.boolean})
+
+    assert a & b == sch.Schema({'a': dt.string, 'c': dt.float64})
+    assert a | b == sch.Schema(
+        {'a': dt.string, 'b': dt.int64, 'c': dt.float64, 'd': dt.boolean, 'e': dt.date}
+    )
+    assert a - b == sch.Schema({'b': dt.int64})
+    assert b - a == sch.Schema({'d': dt.boolean, 'e': dt.date})
+    assert a ^ b == sch.Schema({'b': dt.int64, 'd': dt.boolean, 'e': dt.date})
+
+    assert not a.isdisjoint(b)
+    assert a.isdisjoint(c)
+
+    assert a <= a
+    assert a >= a
+    assert not a < a
+    assert not a > a
+    assert not a <= b
+    assert not a >= b
+    assert not a >= c
+    assert not a <= c
+    assert c <= d
+    assert c < d
+    assert d >= c
+    assert d > c
diff --git a/ibis/tests/expr/test_table.py b/ibis/tests/expr/test_table.py
index d00b8453cf4a..2398c0bba882 100644
--- a/ibis/tests/expr/test_table.py
+++ b/ibis/tests/expr/test_table.py
@@ -1038,7 +1038,8 @@ def test_cross_join(table):
 
     joined = table.cross_join(scalar_aggs)
     agg_schema = api.Schema({'sum_a': 'int64', 'mean_b': 'double'})
-    ex_schema = table.schema().merge(agg_schema)
+    with pytest.warns(FutureWarning):
+        ex_schema = table.schema().merge(agg_schema)
     assert_equal(joined.schema(), ex_schema)