Phase Transition Results for Three Ramsey-Like Theorems

Notre Dame Journal of Formal Logic 57 (2):195-207 (2016)

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.
Keywords finite adjacent Ramsey   Paris–Harrington   Kanamori–McAloon   Ramsey theory   unprovability   independence   phase transitions   Peano arithmetic
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DOI 10.1215/00294527-3452807
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