Fast growing functions based on Ramsey theorems
We present a general framework to define fast growing functions based on Ramsey theorems. This framework is suggested by the work of \textit{J. Ketonen} and \textit{R. Solovay} [Ann. Math., II. Ser. 113, 267-314 (1981; Zbl 0494.03027)] and \textit{A. Kanamori} and \textit{K. McAloon} [Ann. Pure Appl. Logic 33, 23-41 (1987; Zbl 0627.03041)]. One advantage of our approach is that we deal with colorings of pairs. Such colorings may be interpreted as edge colorings of graphs. To appreciate the fast growingness of our functions we need certain sample functions to compare with. These sample functions are defined by ordinal recursion and are in fact generating functions for hierarchies of recursive functions.
scientific article; zbMATH DE number 63145
scientific article