Kurt Gödel Research Center

2012 seminar talk: Shelah's revised power function as a homotopy invariant

Talk held by Misha Gavrilovich (KGRC) at the KGRC seminar on 2012-05-31.

Abstract

In the talk we shall construct a family of partial orders (with extra structure) on <κ-directed families of sets, and express some set theoretic invariants and notions in terms of these partial orders; namely Shelah's revised power function—the cardinal function featuring in Shelah's revised GCH theorem—and the notion of a measurable cardinal.

We shall also try to show that our construction introduces a homotopy-theoretic point of view on these notions: these partial orderings (with the extra structure) satisfy an axiomatization of homotopy theory making them what are known as "model categories", and Shelah's revised power function is what is known as a "homotopy-invariant" "derived functor".