# Category:Class Theory

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This category contains results about **Class Theory**.

Definitions specific to this category can be found in Definitions/Class Theory.

**Class theory** is an extension of set theory which allows the creation of collections that are not sets by classes.

## Subcategories

This category has the following 50 subcategories, out of 50 total.

### A

- Axiom of Infinity (1 P)
- Axiom of Pairing (5 P)
- Axiom of Powers (1 P)
- Axiom of Replacement (4 P)
- Axiom of Swelledness (1 P)

### B

- Basic Universe (6 P)

### C

- Class Difference (2 P)
- Class Theory Work in Progress (45 P)
- Countably Infinite Classes (empty)

### D

- Doubleton Classes (4 P)

### E

- Elements (empty)
- Empty Class (8 P)

### F

- Finite Classes (2 P)

### G

- G-Sets (1 P)
- Gödel-Bernays Class Theory (8 P)

### I

- Infinity (empty)

### M

### N

- Not Every Class is a Set (3 P)

### O

- Ordered Classes (empty)

### P

- Proper Well-Orderings (3 P)

### R

- Relational Closures (6 P)

### S

- Supercomplete Classes (3 P)

### T

- Transitive-Closed Classes (1 P)

### U

- Uncountable (empty)
- Universal Class (3 P)
- Universal Class is Proper (4 P)

### V

### Z

## Pages in category "Class Theory"

The following 45 pages are in this category, out of 45 total.

### C

- Cartesian Product with Proper Class is Proper Class
- Characterization of Class Membership
- Characterization of Minimal Element
- Class Equality is Reflexive
- Class Equality is Symmetric
- Class Equality is Transitive
- Class has Subclass which is not Element
- Class is Extensional
- Class is Not Element of Itself
- Class is Transitive iff Union is Subclass
- Class of All Cardinals is Proper Class
- Collection of Sets Equivalent to Set Containing Empty Set is Proper Class

### E

- Element of Transitive Class
- Element of Universe
- Empty Set is Small
- Epsilon Induction
- Epsilon Relation is Proper
- Epsilon Relation is Strictly Well-Founded
- Existence of Class Complement
- Existence of Class Intersection
- Existence of Class Union
- Existence of Domain of Class Relation
- Existence of Inverse of Class Relation
- Existence of Left Universal Product
- Existence of Middle Universal Product
- Existence of Right Universal Product
- Existence of Right Universal Product/Corollary
- Existence of Universal Class