2008•Mathematical logic quarterlyRequires access

The axiom of choice and the law of excluded middle in weak set theories

John Bell

Abstract

Abstract A weak form of intuitionistic set theoryWSTlacking the axiom of extensionality is introduced. WhileWSTis too weak to support the derivation of the law of excluded middle from the axiom of choice, we show that bee.ng upWSTwith moderate extensionality principles or quotient sets enables the derivation to go through. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Key concepts: Extensionality, Axiom of choice, Constructive set theory, Urelement, Law of excluded middle, Mathematics, Zermelo–Fraenkel set theory, Axiom