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The “world's simplest axiom of choice” fails

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Abstract

We use topos-theoretic methods to show that intuitionistic set theory with countable or dependent choice does not imply that every family, all of whose elements are doubletons and which has at most one element, has a choice function.

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Authors and Affiliations

  1. Department of Mathematics, Columbia University, 10027, New York, NY, USA

    M. P. Fourman

  2. Department of Mathematics, University of Michigan, 48109, Ann Arbor, MI, USA

    A. Ščedrov

Authors
  1. M. P. Fourman
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  2. A. Ščedrov
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Fourman, M.P., Ščedrov, A. The “world's simplest axiom of choice” fails. Manuscripta Math 38, 325–332 (1982). https://doi.org/10.1007/BF01170929

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