WISC may fail in the category of sets

Por • 22 nov, 2013 • Sección: Crítica

David Michael Roberts

Abstract: 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 the very weak choice principle WISC—the statement that for every set there is a set of surjections to it cofinal in all such surjections—is independent of the rest of the axioms of the categorical constructive set theory given by a well-pointed topos.

arXiv:1311.3074v1 [math.CT]

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