|Time:|| 12 - 1:20 p.m.
Department of Mathematical Sciences
Carnegie Mellon University
|Title:||Recent developments in ordinal analysis||
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.