- List of axioms
This is a

**list of**as that term is understood inaxiom smathematics , by Wikipedia page. Inepistemology , the word "axiom" is understood differently; seeaxiom andself-evidence . Individual axioms are almost always part of a largeraxiomatic system .Zermelo-Frankel axioms "These are the"

de facto "standard axioms for contemporarymathematics orset theory . They can be easily adapted to analogous theories, such asmereology ."*

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 schema of specification See also

Zermelo set theory .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***

Hausdorff maximality theorem

*Well-ordering principle

*Zorn's lemma **Weaker than AC***

Axiom of countable choice

*Axiom of dependent choice

*Boolean prime ideal theorem

*Axiom of uniformization **Alternates incompatible with AC***

Axiom of real determinacy **Other axioms of**mathematical logic *

Von Neumann-Bernays-Gödel axioms

*Continuum hypothesis and its generalization

*Freiling's axiom of symmetry

*Axiom of determinacy

*Axiom of projective determinacy

*Martin's axiom

*Axiom of constructibility

*Rank-into-rank

*Kripke-Platek axioms Geometry *

Parallel postulate

*Birkhoff's axioms

*Hilbert's axioms

*Tarski's axioms **Other axioms***

Axiom of Archimedes (real number )

*Axiom of countability (topology )

*Fundamental axiom of analysis (real analysis )

*Gluing axiom (sheaf theory )

*Haag-Kastler axioms (quantum field theory )

*Huzita's axioms (origami )

*Kuratowski closure axioms (topology )

*Peano's axioms (natural numbers )

*Probability axioms

*Separation axiom (topology )

*Wightman axioms (quantum field theory )

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