Combinatorial set theory : partition relations for cardinals
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Bibliographic Information
Combinatorial set theory : partition relations for cardinals
（Studies in logic and the foundations of mathematics, v. 106）
North-Holland Pub. Co. , Sole distributors for the U.S.A. and Canada, Elsevier North-Holland, 1984
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Note
Bibliography: p. [335]-340
Includes indexes
Description and Table of Contents
Description
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.
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.
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