Erdős, Paul - Hajnal András et al.: Combinatorial set theory. Partition relations for cardinals - Disquisitiones mathematicae Hungaricae 13. (Budapest, 1984)

COMBINATORIAL SET THEORY: PARTITION RELATIONS FOR CARDINALS By P. ERDŐS, A. HAJNAL, A. MÁTÉ, R. RADO Ramsey’s classical theorem in its simplest form, published in 1930, says that if we put the edges of an infinite complete graph into two classes, then there will be an infinite complete subgraph, all edges of which belong to the same class. Partition calculus first developed as a collection of generaliza­tions of this theorem. The aim of the authors in writing this book was to present what they consider to be the most important combinatorial ideas in the partition calculus. An introductory chapter deals with the Zermelo-Fraenkel axiom system of set theory and describes the most important tools of set theory used in the book, a section de­scribes the partition symbols most frequently used in literature. A chapter on the applications of combina­torial methods in the partition calculus in­cludes a section on topology, several sections on set mappings and an account of recent inequalities for cardinal powers. AKADÉMIAI KIADÓ BUDAPEST ISBN 963 05 2877 0

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