The weak choice principle WISC may fail in the category of sets
Category Theory
2015-08-27 v4 Logic
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.
Cite
@article{arxiv.1311.3074,
title = {The weak choice principle WISC may fail in the category of sets},
author = {David Michael Roberts},
journal= {arXiv preprint arXiv:1311.3074},
year = {2015}
}
Comments
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-BY