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Line 15:
Line 15: − Mathematicians who find the [[Axiom of Choice]] questionable often replace it with the weaker [[Axiom of Determinacy]]. +
Corrected the claim that AD is a weaker axiom than AC; they are incompatible
Many authors take "Zermelo-Fraenkel" (ZF) to refer to these axioms without the axiom of choice, indicating the inclusion of choice by writing "ZFC".
Many authors take "Zermelo-Fraenkel" (ZF) to refer to these axioms without the axiom of choice, indicating the inclusion of choice by writing "ZFC".
The [[Axiom of Choice]] is independent of (i.e. neither provable nor disprovable from) the Zermelo-Fraenkel axioms. Sometimes alternate axioms are added to ZF, for example the [[Axiom of Determinacy]], which is incompatible with the [[Axiom of Choice]].