Why the Axiom of Choice Sometimes Fails

Logic Journal of the IGPL 28 (6):1207-1217 (2020)
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Abstract

The early controversies surrounding the axiom of choice are well known, as are the many results that followed concerning its dependence from, and equivalence to, other mathematical propositions. This paper focuses not on the logical status of the axiom but rather on showing why it fails in certain categories.

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10.1093/jigpal/jzaa005

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References found in this work

Topoi: The Categorial Analysis of Logic.R. I. Goldblatt - 1982 - British Journal for the Philosophy of Science 33 (1):95-97.
Axioms in Mathematical Practice.Dirk Schlimm - 2013 - Philosophia Mathematica 21 (1):37-92.
Cohesive toposes and Cantor's 'lauter einsen'.F. W. Lawvere - 1994 - Philosophia Mathematica 2 (1):5-15.

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