The weak choice principle WISC may fail in the category of sets
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(Accepted version)
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2015
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Roberts, D.
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Studia Logica, 2015; 103(5):1005-1017
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David Michael Roberts
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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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© Springer Science+Business Media Dordrecht 2015