David Roberts Con(ZF+not WISC)

This is the webpage for the currently-being-written paper Con(ZF+$\neg$WISC). See also the nLab page for WISC.

• Con(ETCS-AC+neg WISC)

  • As it stands, I haven’t yet shown independence from ZF. The notes at present do show that WISC is independent of category-theoretic axioms for sets such as ETCS minus the axiom of choice, and probably also the same plus the relevant form of the axiom of separation.

Further developments will be worked out here. Some thoughts can be seen, if you really want to read them, in the previous version of this page.

References

Shulman’s paper on stack semantics.

Dorais’ formulation of WISC

van den Berg’s note that proved the consistency of $\neg$ WISC relative to large cardinals (using Gitik’s model).

Karagila’s paper showing consistency of $\neg$ WISC using a variant on models of Monro, Rathjen and Roguski.