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The Weak Choice Principle WISC may Fail in the Category of Sets

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Abstract

The set-theoretic axiom WISC states that for every set there is a set of surjections to it cofinal in all such surjections. By constructing an unbounded topos over the category of sets and using an extension of the internal logic of a topos due to Shulman, we show that WISC is independent of the rest of the axioms of the set theory given by a well-pointed topos. This also gives an example of a topos that is not a predicative topos as defined by van den Berg.

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  1. School of Mathematical Sciences, The University of Adelaide, Adelaide, SA, 5005, Australia

    David Michael Roberts

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  1. David Michael Roberts
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Correspondence to David Michael Roberts.

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This is the final published version of the preprint arXiv:1311.3074.

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Roberts, D.M. The Weak Choice Principle WISC may Fail in the Category of Sets. Stud Logica 103, 1005–1017 (2015). https://doi.org/10.1007/s11225-015-9603-6

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  • DOI: https://doi.org/10.1007/s11225-015-9603-6

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