Introduction to Cardinal Arithmetic

Description

This book is an introduction to modern cardinal arithmetic in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice. A first part describes the classical theory developed by Bernstein, Cantor, Hausdorff, König and Tarski between 1870 and 1930. Next, the development in the seventies led by Galvin, Hajnal and Silver is characterized. The third part presents the fundamental investigations in pcf theory which have been worked out by Shelah to answer the questions left open n the seventies.

This text is the first self-contained introduction to cardinal arithmetic which also includes pcf theory. It is aimed at undergraduate, and also postgraduate students as well as researchers who want to broaden their knowledge of cardinal arithmetic. It gives a relatively complete survey of results provable in ZFC.

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