Introduction to Cardinal Arithmetic

Michael Holz, Karsten Steffens, E. Weitz9783764361242, 9780817661243, 0817661247, 3764361247

This book is an introduction into modern cardinal arithmetic in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice (ZFC). A first part describes the classical theory developed by Bernstein, Cantor, Hausdorff, König and Tarski between 1870 and 1930. Next, the development in the 1970s 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 in the 1970s.

Reviews:

“The authors aim their text at beginners in set theory. They start literally from the axioms and prove everything they need. The result is an extremely useful text and reference book which is also very pleasant to read.” – The Bulletin of Symbolic Logic

“The book should be required reading for every advanced graduate student of set theory. Several courses at various levels could be based on the earlier chapters. There is a useful set of exercises at the end of most sections in the first four chapters.” – Mathematical Reviews