Kurt Gödel Research Center

2018 seminar talk: From fixed points in weak set theories to some open problems

Talk held by Gerhard Jäger (Universität Bern, Switzerland) at the KGRC seminar on 2018-10-09.

Abstract

Least fixed points of monotone operators are well-studied objects in many areas of mathematical logic. Typically, they are characterized as the intersection of all sets closed under the respective operator or as the result of its iteration from below.

In this talk I will start off from specific $\Sigma_1$ operators in a Kripke-Platek environment and relate fixed point assertions to alternative set existence principles. By doing that, we are also led to some “largeness axioms” and to several open problems.