# Category:Set theory

Here is a list of articles in the Set theory category of the Computing portal that unifies foundations of mathematics and computations using computers.

**Set theory**is any of a number of subtly different things in mathematics:

- Naive set theory is the original set theory developed by mathematicians at the end of the 19th century, treating sets simply as collections of things.
- Axiomatic set theory is a rigorous axiomatic theory developed in response to the discovery of serious flaws (such as Russell's paradox) in naive set theory. It treats sets as "whatever satisfies the axioms", and the notion of collections of things serves only as motivation for the axioms.
- Internal set theory is an axiomatic extension of set theory that supports a logically consistent identification of
*illimited*(enormously large) and*infinitesimal*elements within the real numbers. - Various versions of logic have associated sorts of sets (such as fuzzy sets in fuzzy logic).

## Subcategories

This category has the following 9 subcategories, out of 9 total.

### A

### C

### D

### F

### I

### O

### S

## Pages in category "Set theory"

The following 142 pages are in this category, out of 142 total.

- Set theory
*(computing)*

### *

- Set (mathematics)
*(computing)*

### A

- Admissible set
*(computing)* - Almost
*(computing)*

### B

- Baire space
*(computing)* - Benacerraf's identification problem
*(computing)* - BIT predicate
*(computing)* - Boolean differential calculus
*(computing)*

### C

- Cabal (set theory)
*(computing)* - Cantor's diagonal argument
*(computing)* - Cantor's first set theory article
*(computing)* - Cantor's paradise
*(computing)* - Cantor's theorem
*(computing)* - Cardinal assignment
*(computing)* - Cardinality of the continuum
*(computing)* - Categorical set theory
*(computing)* - Chang's conjecture
*(computing)* - Class (set theory)
*(computing)* - Class logic
*(computing)* - Club filter
*(computing)* - Club set
*(computing)* - Clubsuit
*(computing)* - Code (set theory)
*(computing)* - Cofinality
*(computing)* - Condensation lemma
*(computing)* - Conglomerate (mathematics)
*(computing)* - Conglomerate (set theory)
*(computing)* - Continuous function (set theory)
*(computing)* - Continuum (set theory)
*(computing)* - Controversy over Cantor's theory
*(computing)* - Cumulative hierarchy
*(computing)* - Cylinder (algebra)
*(computing)*

### D

- Deductive closure
*(computing)* - Definable real number
*(computing)* - Diaconescu's theorem
*(computing)* - Diagonal intersection
*(computing)* - Diamond principle
*(computing)* - Dimensional operator
*(computing)*

### E

- Easton's theorem
*(computing)* - Equaliser (mathematics)
*(computing)* - Equivalence class
*(computing)* - Erdős–Rado theorem
*(computing)* - Erdős–Dushnik–Miller theorem
*(computing)* - Extension (semantics)
*(computing)* - Extensionality
*(computing)*

### F

- Finitist set theory
*(computing)* - Fodor's lemma
*(computing)*

### G

- Game-theoretic rough sets
*(computing)* - Georg Cantor's first set theory article
*(computing)* - Glossary of set theory
*(computing)* - Gödel logic
*(computing)* - Goodstein's theorem
*(computing)*

### H

- Hartogs number
*(computing)* - Hausdorff Medal
*(computing)* - Hausdorff gap
*(computing)* - Hereditarily countable set
*(computing)* - Hereditarily finite set
*(computing)* - Hereditary property
*(computing)* - Hereditary set
*(computing)* - Hume's principle
*(computing)*

### I

- Ideal (set theory)
*(computing)* - Implementation of mathematics in set theory
*(computing)* - Infinitary combinatorics
*(computing)* - Information diagram
*(computing)*

### J

- Jensen's covering theorem
*(computing)* - Jónsson function
*(computing)*

### K

- Kuratowski's free set theorem
*(computing)*

### L

- Laver function
*(computing)* - Lévy hierarchy
*(computing)* - Limit cardinal
*(computing)* - List of exceptional set concepts
*(computing)* - List of set theory topics
*(computing)* - List of statements independent of ZFC
*(computing)*

### M

- Mathematical structure
*(computing)* - Mengenlehreuhr
*(computing)* - Milner–Rado paradox
*(computing)* - Morass (set theory)
*(computing)* - Mostowski model
*(computing)* - Multiplicity (mathematics)
*(computing)* - Multiverse (set theory)
*(computing)*

### N

- Naive set theory
*(computing)* - Named set theory
*(computing)* - Nested set
*(computing)* - Normal function
*(computing)* - Null set
*(computing)*

### O

- Ω-logic
*(computing)* - Ontological maximalism
*(computing)* - Ordinal arithmetic
*(computing)* - Ordinal definable set
*(computing)*

### P

- Pairing function
*(computing)* - Pantachy
*(computing)* - Paradoxes of set theory
*(computing)* - The Paradoxes of the Infinite
*(computing)* - Paradoxical set
*(computing)* - PCF theory
*(computing)* - Permutation model
*(computing)* - Preordered class
*(computing)* - Primitive notion
*(computing)* - Primitive recursive set function
*(computing)* - Pseudo-intersection
*(computing)*

### Q

- Quasi-set theory
*(physics)* - Willard Van Orman Quine
*(biography)*

### R

- Recursive ordinal
*(computing)* - Reflection principle
*(computing)*

### S

- S (set theory)
*(computing)* - Schröder–Bernstein property
*(computing)* - Scott's trick
*(computing)* - Separating set
*(computing)* - Set intersection oracle
*(computing)* - Set notation
*(computing)* - Set theory of the real line
*(computing)* - Set Theory: An Introduction to Independence Proofs
- Set-builder notation
*(computing)* - Set-theoretic limit
*(computing)* - Set-theoretic topology
*(computing)* - Sierpiński set
*(computing)* - Signed set
*(computing)* - Soft set
*(computing)* - Solovay model
*(computing)* - Square principle
*(computing)* - Stationary set
*(computing)* - Stratification (mathematics)
*(computing)* - Structuralism (philosophy of mathematics)
*(philosophy)* - Subclass (set theory)
*(computing)* - Successor cardinal
*(computing)* - Sunflower (mathematics)
*(computing)* - Superstrong cardinal
*(computing)* - Supertransitive class
*(computing)* - Support (mathematics)
*(computing)* - Suslin representation
*(computing)*

### T

- Tail sequence
*(computing)* - Tarski's theorem about choice
*(computing)* - Theory of regions
*(computing)* - Total order
*(computing)* - Transitive model
*(computing)* - Transitive reduction
*(computing)* - Transitive set
*(computing)* - Tree (set theory)
*(computing)*

### U

- Ulam matrix
*(computing)* - Uniformization (set theory)
*(computing)* - Universe (mathematics)
*(computing)*

### V

- Vicious circle principle
*(computing)*