# List of axioms

This is a**list of axioms**as that term is understood in mathematics, by Wikipedia page. In epistemology, the word

*axiom*is understood differently; see axiom and self-evidence. Individual axioms are almost always part of a larger axiomatic system.

Table of contents |

2 Axiom of choice 3 Other axioms of mathematical logic 4 Other axioms |

## Zermelo-Frankel axioms

*These are the*de facto

*standard axioms for contemporary mathematics*

- Axiom of extensionality
- Axiom of empty set
- Axiom of pairing
- Axiom of union
- Axiom of infinity
- Axiom schema of replacement
- Axiom of power set
- Axiom of regularity
- Axiom of separation

## Axiom of choice

*With the Zermelo-Frankel axioms above, this makes up the system ZFC in which most mathematics is potentially formalisable*

### Equivalents of AC

### Weaker than AC

### Alternates incompatible with AC

## Other axioms of mathematical logic

## Other axioms