Mathematical Logic Quarterly 54 (2):194-201 (2008)

John L. Bell
University of Western Ontario
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 up WST with moderate extensionality principles or quotient sets enables the derivation to go through
Keywords Axiom of choice  law of excluded middle  axiom of extensionality  weak set theory
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DOI 10.1002/malq.200710030
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References found in this work BETA

Choice Implies Excluded Middle.N. Goodman & J. Myhill - 1978 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 24 (25-30):461-461.
Choice Implies Excluded Middle.N. Goodman & J. Myhill - 1978 - Mathematical Logic Quarterly 24 (25‐30):461-461.
Extensionality Versus Constructivity.Silvio Valentini - 2002 - Mathematical Logic Quarterly 48 (2):179-187.
On the Axiom of Extensionality – Part I.R. O. Gandy - 1956 - Journal of Symbolic Logic 21 (1):36-48.

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The Axiom of Choice.John L. Bell - 2008 - Stanford Encyclopedia of Philosophy.

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