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

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

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10.1002/malq.200710030

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John L. Bell
University of Western Ontario

Citations of this work

The axiom of choice.John L. Bell - 2008 - Stanford Encyclopedia of Philosophy.

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References found in this work

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.
On the axiom of extensionality – Part I.R. O. Gandy - 1956 - Journal of Symbolic Logic 21 (1):36-48.
On the axiom of extensionality, part II.R. O. Gandy - 1959 - Journal of Symbolic Logic 24 (4):287-300.

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