Axiom of determinacy

In mathematics, the axiom of determinacy (abbreviated as AD) is an axiom in set theory. It states the following:

Related Topics:
Mathematics - Axiom - Set theory

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The axiom of determinacy is inconsistent with the axiom of choice (AC); however, it has been shown that it implies that all sets of reals are Lebesgue measurable and have the property of Baire.

Related Topics:
Axiom of choice - Real - Lebesgue measurable - Property of Baire

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AD implies the consistency of ZF. Hence it is not possible to prove in ZF that ZF is consistent with AD.

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