Ernest Schimmerling

Mathematical logic seminar - November 3, 2005

Time: 12 - 1:20 p.m.

Room: OSC 201

Speaker: Henry Towsner
Department of Mathematical Sciences
Carnegie Mellon University

Title: Recent developments in ordinal analysis

Abstract: Ordinal analysis is the branch of proof theory which finds bounds for the longest provable well-orderings in a theory, providing a measurement for the consistency strength of a theory. In the last few decades, the area of interest has shifted from subsystems of second order arithmetic to extensions of Kripke-Platek set theory.

In the mid-90's, this work culminated in the analysis of theories equiconsistent with the theory of Pi-1-2 Comprehension. I will outline the major elements of the work leading up to this result, with a particular focus on set-theoretic elements, especially the interaction with recursive analogs of large-cardinal axioms.