EM + Ext_ + AC~i~n~t is equivalent to AC~e~x~t

Mathematical Logic Quarterly 50 (3):236 (2004)
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Abstract

It is well known that the extensional axiom of choice implies the law of excluded middle. We here prove that the converse holds as well if we have the intensional axiom of choice ACint, which is provable in Martin-Löf's type theory, and a weak extensionality principle, which is provable in Martin-Löf's extensional type theory. In particular, EM is equivalent to ACext in extensional type theory.

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10.1002/malq.200410100

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Citations of this work

A minimalist two-level foundation for constructive mathematics.Maria Emilia Maietti - 2009 - Annals of Pure and Applied Logic 160 (3):319-354.
2006 Annual Meeting of the Association for Symbolic Logic.Matthew Valeriote - 2007 - Bulletin of Symbolic Logic 13 (1):120-145.

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References found in this work

Choice Implies Excluded Middle.N. Goodman & J. Myhill - 1978 - Mathematical Logic Quarterly 24 (25‐30):461-461.
Choice Implies Excluded Middle.N. Goodman & J. Myhill - 1978 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 24 (25-30):461-461.

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