On proof-theoretic dilator and Pohlers’ characteristic ordinals

Hanul Jeon (Cornell U, Ithaca)

Jul 01. 2025, 14:00 — 14:45

The proof-theoretic ordinal (PTO) of a theory is a way to gauge the strength by looking at the supremum of provably well-founded recursive ordinals. There are two generalizations of the PTO: Pohlers isolated characteristic ordinals in “On the Performance of Axiom Systems,” which is the supremum of provably well-founded definable well-orders over a given Spector class. Meanwhile, Girard developed another invariant of a theory called proof-theoretic dilator that also yields PTO. In this talk, I will demonstrate proof-theoretic dilators are related to Pohlers’ characteristic ordinals.

Further Information
Venue:
ESI Schrödinger and Boltzmann Lecture Hall
Associated Event:
Reverse Mathematics (Thematic Programme)
Organizer(s):
Juan Aguilera (TU Vienna)
Linda Brown Westrick (Penn State U)
Noam Greenberg (Victoria U of Wellington)
Denis Hirschfeldt (U of Chicago)