Phase transition results for three Ramsey-like theorems

Abstract

We classify a sharp phase transition threshold for Friedman's finite adjacent Ramsey theorem. We extend the method for showing this result to two previously known classifications involving Ramsey theorem variants: the Paris--Harrington theorem and the Kanamori--McAloon theorem. We also provide tools to remove ad-hoc arguments from the proofs of phase transition results as much as currently possible.

This is the pre-peer reviewed version of a paper which has been accepted for publication at the Notre Dame Journal of Formal Logic (2016)