We classify a sharp phase transition threshold for Friedman’s finite adjacent Ramsey theorem. We extend the method for showing this result to two previous 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.
"Phase Transition Results for Three Ramsey-Like Theorems." Notre Dame J. Formal Logic 57 (2) 195 - 207, 2016. https://doi.org/10.1215/00294527-3452807