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List of axioms

From Wikipedia, the free encyclopedia

This is alist ofaxioms as that term is understood inmathematics. Inepistemology, the wordaxiom is understood differently; seeaxiom andself-evidence. Individual axioms are almost always part of a largeraxiomatic system.

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

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Together with the axiom of choice (see below), these are thede factostandard axioms for contemporarymathematics orset theory. They can be easily adapted to analogous theories, such asmereology.

See alsoZermelo set theory.

Axiom of choice

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

Equivalents of AC

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Stronger than AC

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Weaker than AC

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Alternates incompatible with AC

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Other axioms ofmathematical logic

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Geometry

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Other axioms

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See also

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