Keita Yokoyama - First-order strength of Ramsey's theorem for pairs---from the perspective....

This lecture was part of the Workshop on "Reverse Mathematics: New Paradigms" held at the ESI August 4 - 8, 2025.

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.

Видео Keita Yokoyama - First-order strength of Ramsey's theorem for pairs---from the perspective.... канала Erwin Schrödinger International Institute for Mathematics and Physics (ESI)