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Combinatorial Set Theory: Partition Relations for Cardinals - 1st Edition - ISBN: 9780444861573, 9780444537454

Combinatorial Set Theory: Partition Relations for Cardinals, Volume 106

1st Edition

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Authors: P. Erdös A. Máté A. Hajnal P. Rado
eBook ISBN: 9780444537454
Imprint: North Holland
Published Date: 1st May 1984
Page Count: 348
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Table of Contents

Fundamentals about Partition Relations. Trees and Positive Ordinary Partition Relations. Negative Ordinary Partition Relations and the Discussion of the Finite Case. The Canonization Lemmas. Large Cardinals. Discussion of the Ordinary Partition Relation with Superscript 2. Discussion of the Ordinary Partition Relation with Superscript > 3. Some Applications of Combinatorial Methods. A Brief Survey of the Square Bracket Relation.


This work presents the most important combinatorial ideas in partition calculus and discusses ordinary partition relations for cardinals without the assumption of the generalized continuum hypothesis. A separate section of the book describes the main partition symbols scattered in the literature. A chapter on the applications of the combinatorial methods in partition calculus includes a section on topology with Arhangel'skii's famous result that a first countable compact Hausdorff space has cardinality, at most continuum. Several sections on set mappings are included as well as an account of recent inequalities for cardinal powers that were obtained in the wake of Silver's breakthrough result saying that the continuum hypothesis can not first fail at a singular cardinal of uncountable cofinality.


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© North Holland 1984
1st May 1984
North Holland
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@qu:Its appearance is welcome... fills a long-standing gap in the contemporary set-theoretical literature. @source:Mathematical Reviews @qu:...should remain the standard reference for ordinary partition relations for a long time. @source:Periodica Mathematica Hungarica

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About the Authors

P. Erdös

A. Máté

A. Hajnal

P. Rado

Affiliations and Expertise

Formerly Research Manager, the Worcester Royal Procelain Company Ltd., Worcester, UK