Synopsis
This book is an introduction to modern cardinal arithmetic, developed in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice. Part two, which is Chapter 2, characterizes the development of cardinal arith metic in the seventies, which was led by Galvin, Hajnal, and Silver.
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Review
From 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
“The book under review, while truly an introduction to the beautiful subject of cardinal arithmetic ... . the reader should really want to become a set theorist himself, if he’s to go any real distance with this book. But there are lots of exercises (that look pretty sporty to me), and the authors have taken great pains to prove everything very carefully and thoroughly. It’s obviously a fine source for those inclined to go this route.” (Michael Berg, The Mathematical Association of America, April, 2010)
Synopsis
This text is an introduction to cardinal arithmetic which also includes pcf theory. It gives a relatively complete survey of results provable in ZFC.
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