First-order strength of Ramsey's theorem for pairs---from the perspective of proof size

Keita Yokoyama (Tohoku U)

Aug 04. 2025, 15:50 — 16:50

In the study of reverse mathematics, numerous conservation theorems are established using low basis theorems and their variations. Specifically, the proof-theoretic/first-order strength of Ramsey's theorem for pairs and its variations are calibrated in this way. In this talk, we introduce a method for converting model-theoretic Pi^1_1-conservation theorems by means of low-like basis theorems into proof interpretations. We will then overview the study of the first-order strength of Ramsey's theorem for pairs and reproving several conservation theorems together with polynomial-size proof transformations.

 

Further Information
Venue:
ESI Schrödinger and Boltzmann Lecture Hall
Recordings:
Recording
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)