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Classifying the phase transition threshold for unordered regressive Ramsey numbers

By Florian Pelupessy and Andreas Weiermann


Following ideas of Richer (2000) we introduce the notion of unordered regressive Ramsey numbers or unordered Kanamori-McAloon numbers. We show that these are of Ackermannian growth rate. For a given number-theoretic function f we consider unordered f-regressive Ramsey numbers and classify exactly the threshold for f which gives rise to the Acker-mannian growth rate of the induced f-regressive Ramsey numbers. This threshold coincides with the corresponding threshold for the standard re-gressive Ramsey numbers. Our proof is based on an extension of an argumtent from a corresponding proof in a paper by Kojman,Lee,Omri and Weiermann 2007.

Year: 2014
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