Färbungen großer Würfel mit bunten Wegen
type: Item
instance of: scholarly article
title: Färbungen großer Würfel mit bunten Wegen
zbMATH Open document ID: 0542.03027
DOI: 10.1007/BF01192825
author: Kurt Wolfsdorf
published in: Archiv der Mathematik
publication date: 1983-01-01T00:00:00Z
review text: In 1976 V. Rödl and J. Nešetřil asked whether there exists a cardinal number k such that for every mapping \(f:\prod_{k}I\to \{0,1\}\) there exists an embedding e of the real unit interval I into \(I^ k\) such that \(f\circ e\) is constant. The question was answered by \textit{W. Weiss} [Topology, Vol. II, 4th Colloq. Budapest 1978, Colloq. Math. Soc. János Bolyai 23, 1249-1255 (1980; Zbl 0434.54011)] and independently by the author [Habilitationsschrift (1981)]. The paper contains a proof of Theorem 1: Let k be a cardinal in \([\omega,(2^{\omega})^{(+\omega)}]\) and T a \(T_ 2\)-space of power k; then there is a mapping \(f:T\to 2^{\omega}\) such that for every embedding \(e: L\to T\) one has \((f\circ e)''I=2^{\omega}.\) The author formulates a principle \(*_ k\) and proves that for every \(k>0\) one has \(Con(ZFC)\Rightarrow Con(ZFC+CH+*_ k+\neg GCH)\) (Theorem 3).
Mathematics Subject Classification ID: 03E35
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 03E50
Mathematics Subject Classification ID: 03E65
Mathematics Subject Classification ID: 54A25
zbMATH DE Number: 3861141
zbMATH Keywords: partition embedding principle
zbMATH Keywords: generalized continuum hypothesis
MaRDI profile type: Publication
cites work: Aspects of constructibility
cites work: Intersection Theorems for Systems of Sets
cites work: Ein Zerlegungssatz für P(\(\kappa\) )
cites work: Countably Compact Spaces and Martin's Axiom
description: scientific article; zbMATH DE number 3861141