- List of axioms
This is a list of
axiom s as that term is understood inmathematics , 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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