Unordered Canonical Ramsey Numbers

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 numbertheoretic function f we consider unordered f-regressive Ramsey numbers and classify exactly the threshold for f which gives rise to the Ackermannian growth rate of the induced f-regressive Ramsey numbers. This threshold coincides with the corresponding threshold for the standard regressive 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.

• Type: Journal
• Year: 2000
• Where: JCT
• Authors: Duncan C. Richer
• Keywords: F-regressive Ramsey Numbers, JCT 2000, Ramsey Numbers, Regressive Ramsey Numbers