Category:Set Theory
This category contains results about Set Theory.
Definitions specific to this category can be found in Definitions/Set Theory.
Set Theory is the branch of mathematics which studies sets.
Subcategories
This category has the following 74 subcategories, out of 74 total.
A
B
C
D
E
F
H
I
L
M
N
O
P
Q
R
S
T
U
V
Pages in category "Set Theory"
The following 113 pages are in this category, out of 113 total.
A
- Absorption Laws
- Analog between Logic and Set Theory
- Axiom:Axiom of Choice for Finite Sets
- Axiom:Axiom of Choice for Finite Sets/Proof from Hall's Marriage Theorem
- Axiom:Axiom of Choice for Finite Sets/Proof from Ordering Principle
- Axiom of Choice Implies Axiom of Dependent Choice
- Axiom of Choice Implies Law of Excluded Middle
- Axiom of Choice Implies Zorn's Lemma
- Axiom of Dependent Choice Implies Axiom of Countable Choice
C
- Cantor-Bernstein-Schröder Theorem
- Cardinality Less One
- Cardinality of Finite Set is Well-Defined
- Cardinality of Integer Interval
- Cardinality of Power Set of Natural Numbers Equals Cardinality of Real Numbers
- Cardinality of Proper Subset of Finite Set
- Cardinality of Subset of Finite Set
- Cardinality of Subset Relation on Power Set of Finite Set
- Cartesian Product of Countable Sets is Countable
- Cartesian Product of Natural Numbers with Itself is Countable
- Cartesian Product Preserves Cardinality
- Choice Function Exists for Set of Well-Ordered Sets
- Choice Function Exists for Well-Orderable Union of Sets
- Complex Numbers are Uncountable
- Continuum Hypothesis
- Correspondence Theorem (Set Theory)
- Cowen-Engeler Lemma
D
E
F
H
I
- Image Filter is Filter
- Image of Ultrafilter is Ultrafilter
- Increasing Sequence of Sets induces Partition on Limit
- Induction of Finite Set
- Inner Limit in Hausdorff Space by Open Neighborhoods
- Inner Limit in Hausdorff Space by Set Closures
- Inverse Image of Set under Set-Like Relation is Set
- Isomorphism to Closed Interval
O
R
S
- Set Equality is Equivalence Relation
- Set Equals Itself
- Set Equation: Intersection
- Set Equation: Union
- Set Equivalence is Equivalence Relation
- Set Finite iff Injection to Initial Segment of Natural Numbers
- Set Finite iff Surjection from Initial Segment of Natural Numbers
- Set Inequality
- Set is Equivalent to Image under Injection
- Set is Small Class
- Set of Chains is Chain Complete for Inclusion
- Set of Subsets is Cover iff Set of Complements is Free
- Singleton Equality
- Skolem's Paradox
- Subset of Empty Set
- Subset of Finite Set is Finite
- Subset of Naturals is Finite iff Bounded
- Substitution of Elements
- Substitutivity of Equality
- Successor Set of Transitive Set is Transitive
- Superset of Co-Countable Set
- Superset of Infinite Set is Infinite
