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

✍ Scribed by John L. Bell

Publisher: John Wiley and Sons
Year: 2008
Tongue: English
Weight: 116 KB
Volume: 54
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200710030

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✦ Synopsis

Abstract

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

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