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.Comment: v2 Change of title and abstract; v3 Almost completely rewritten after
referee pointed out critical mistake. v4 Final version. Will be published in
Studia Logica. License is CC-B
