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arXiv · 1311.3074

The weak choice principle WISC may fail in the category of sets

David Michael Roberts
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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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David Michael Roberts. 2013-11-13. The weak choice principle WISC may fail in the category of sets. https://doi.org/10.1007/s11225-015-9603-6

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