This is a list of axioms as that term is understood in mathematics. In epistemology, the word axiom is understood differently; see axiom and self-evidence. Individual axioms are almost always part of a larger axiomatic system.

ZF (the Zermelo–Fraenkel axioms without the axiom of choice)

Together with the axiom of choice (see below), these are the de facto standard axioms for contemporary mathematics or set theory. They can be easily adapted to analogous theories, such as mereology.

See also Zermelo set theory.

Axiom of choice

With the Zermelo–Fraenkel axioms above, this makes up the system ZFC in which most mathematics is potentially formalisable.

Equivalents of AC

Stronger than AC

Weaker than AC

Alternates incompatible with AC

Other axioms of mathematical logic


Other axioms

See also