A short proof of a partion relation for triples
type: Item
instance of: scholarly article
title: A short proof of a partion relation for triples
zbMATH Open document ID: 0945.03067
author: Albin L. Jones
published in: The Electronic Journal of Combinatorics
publication date: 2000-05-11T00:00:00Z
full work available at URL: https://eudml.org/doc/120506
full work available at URL: v7i1r24.html
review text: A very nice elementary proof is given for the following theorem due (essentially) to Erdős and Rado: if \(\varphi\) is an order type with \(\varphi\to(\eta)^1_\omega\) then \(\varphi\to(\omega+n,4)^3\) holds for \(n<\omega\). It is also shown that if \(\varphi\) is an order type and \(\kappa\) an infinite cardinal then \(\varphi\not\to(\omega)^1_{2^\kappa}\) implies \(\varphi\to(\kappa+2,\omega)^3\) and \(\varphi\not\to\left(\text{cf}(\kappa)\right)^1_{\kappa}\) implies \(\varphi\to(\kappa+1,4)^3\).
Mathematics Subject Classification ID: 03E02
Mathematics Subject Classification ID: 05D10
zbMATH DE Number: 1446316
zbMATH Keywords: partition relations
zbMATH Keywords: ordered sets
reviewed by: Péter Komjáth
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1446316