# Category:Set Theory

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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 89 subcategories, out of 89 total.

### A

- Aleph Mapping (11 P)

### B

### C

- Combinations with Repetition (1 P)
- Combinatorial Set Theory (empty)
- Comparable Sets (empty)
- Continuum Hypothesis (2 P)
- Covers (6 P)

### D

- Descriptive Set Theory (empty)
- Disjoint Unions (1 P)
- Doubletons (11 P)

### E

- Enumerations (empty)
- Equivalents of the Axiom of Choice (empty)
- Examples in Set Theory (10 P)

### F

- Fuzzy Set Theory (1 P)

### H

- Hartogs' Lemma (Set Theory) (3 P)

### I

- Inner Model Theory (1 P)

### L

- Limits of Sets (2 P)

### M

- Membership Relation (3 P)
- Minimal Infinite Successor Set (14 P)

### N

- Nested Sequences (1 P)
- Nests (1 P)

### O

- Order-Extension Principle (3 P)
- Ordered Pairs (5 P)
- Ordering Principle (3 P)
- Ordinary Sets (2 P)

### P

### Q

### R

### S

### T

- Transfinite Arithmetic (4 P)

### U

- Universe (9 P)

### V

## Pages in category "Set Theory"

The following 109 pages are in this category, out of 109 total.

### A

### 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
- 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

### O

### R

### S

- Set Equality is Equivalence Relation
- Set Equation: Intersection
- Set Equation: Union
- 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
- Smallest Set is Unique
- Smallest Set may not Exist
- Strictly Well-Founded Relation has no Relational Loops
- Substitution of Elements
- Substitutivity of Equality
- Successor Set of Transitive Set is Transitive
- Superset of Co-Countable Set
- Superset of Infinite Set is Infinite