Kurt Gödel Research Center

Synonymy, Stratification and the Universal Set

Talk held by Thomas Forster (Queens' College and DPMMS, Cambridge, UK) at the KGRC Friday seminar on 2019‑03‑15.

Abstract

Set theories that radically contradict one another (“Are there atoms or not? Is there a Universal Set or not? Is set membership wellfounded or not?”) can nevertheless be synonymous. But does that not mean that they are reporting to us on the same mathematics? So just what is at stake with these disagreements? As we uncover more of these synonymy results it is starting to look as if the parts that are not at stake can be captured by stratifiable expressions. It turns out that this is an echo of the strong typing of mathematics. The nonexistence of the Universal Set is no more part of Mathematics than was the idea that 3 is a member of 5.

A video recording of this talk is available on YouTube.

A handout for this talk is available here.