Fast growing functions based on Ramsey theorems
type: Item
instance of: scholarly article
title: Fast growing functions based on Ramsey theorems
zbMATH Open document ID: 0758.03019
DOI: 10.1016/0012-365X(91)90346-4
author: W. Thumser
author: Bernd Voigt
author: Hans Jürgen Prömel
published in: Discrete Mathematics
publication date: 1992-09-27T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 03D20
Mathematics Subject Classification ID: 05D10
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 03D60
zbMATH DE Number: 63145
zbMATH Keywords: fast growing functions
zbMATH Keywords: Ramsey theorems
zbMATH Keywords: colorings of pairs
zbMATH Keywords: edge colorings of graphs
zbMATH Keywords: ordinal recursion
zbMATH Keywords: hierarchies of recursive functions
MaRDI profile type: Publication
Wikidata QID: Q59409091
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full work available at URL: 0012-365x(91)90346-4
OpenAlex ID: W1968730206
description: scientific article; zbMATH DE number 63145