Combinatorial Set Theory: Partition Relations for Cardinals book cover

Combinatorial Set Theory: Partition Relations for Cardinals

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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Published: May 1984

Imprint: North-holland

ISBN: 978-0-444-86157-3

Reviews

  • Its appearance is welcome... fills a long-standing gap in the contemporary set-theoretical literature.
    Mathematical Reviews


    ...should remain the standard reference for ordinary partition relations for a long time.
    Periodica Mathematica Hungarica

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.

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