Combinatorial Set Theory: Partition Relations for Cardinals

P. Erdös, A. Máté, A. Hajnal, P. Rado

• Publisher: North Holland
• Year: 2011
• Print ISBN:
  9780444861573
• eBook ISBN:
  9780444537454
• Topic: Mathematics
• Subtopic: Discrete Mathematics
• Index: Mathematics

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

• Front Cover
• Combinatorial Set Theory: Partition Relations for Cardinals
• Copyright Page
• Contents
• Preface
• Chapter I. Introduction
• Chapter II. Preliminaries
• Chapter III. Fundamentals about partition relations
• Chapter IV. Trees and positive ordinary partition relations
• Chapter V. Negative ordinary partition relations, and the discussion of the finite case
• Chapter VI. The canonization lemmas
• Chapter VII. Large cardinals
• Chapter VIII. Discussion of the ordinary partition relation with superscript 2
• Chapter IX. Discussion of the ordinary partition relation with superscript G 3
• Chapter X. Some applications of combinatorial metbods
• Chapter XI. A brief survey of the square bracket relation
• Bibliography
• Author index
• Subject index