Introduction To Cardinal Arithmetic by Michael HolzIntroduction To Cardinal Arithmetic by Michael Holz

Introduction To Cardinal Arithmetic

byMichael Holz, Karsten Steffens, E. Weitz

Book & Audio | November 23, 2009

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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
Title:Introduction To Cardinal ArithmeticFormat:Book & AudioDimensions:304 pagesPublished:November 23, 2009Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3034603274

ISBN - 13:9783034603270

Reviews

Table of Contents

Preface.- Introduction.- Foundations.- The Galvin-Hajnal Theorem.- Ordinal Functions.- Approximation Sequences.- pcf-Theory.- Local Properties.- Applications.- The Cardinal Function.

Editorial Reviews

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)