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

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