Item description for The Higher Infinite: Large Cardinals in Set Theory from Their Beginnings (Springer Monographs in Mathematics) by Akihiro Kanamori...
The theory of large cardinals is currently a broad mainstream of modern set theory, the main area of investigation for the analysis of the relative consistency of mathematical propositions and possible new axioms for mathematics. The first of a projected multi-volume series, this book provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowthsleadingto the frontiers of contemporary research. A "genetic" approach is taken, presenting the subject in the context of its historical development. With hindsight the consequential avenues are pursued and the most elegant or accessible expositions given. With open questions and speculations provided throughout the reader should not only come to appreciate the scope and coherence of the overall enterprise but also become prepared to pursue research in several specific areas by studying the relevant sections.
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Est. Packaging Dimensions: Length: 1.25" Width: 6.5" Height: 9.25" Weight: 2.1 lbs.
Release Date Jul 29, 2003
ISBN 3540003843 ISBN13 9783540003847
Reviews - What do customers think about The Higher Infinite: Large Cardinals in Set Theory from Their Beginnings (Springer Monographs in Mathematics)?
large cardinals Jul 11, 2008
If you have background in set theory the book is ok if not then it's difficult reading
A must have Oct 2, 2005
A must have for set theorists. Does a better job than Jech. It's a little weird how you get a sense of the set theorists as people, but the historical stuff is otherwise really great.
Interesting but too much reading Jul 12, 2005
Assumes set theory through forcing and some model theory. He integrates a lot of historical information which is interesting but greatly adds to the reading without adding to the mathematical understanding. The semester is short and I want to learn what I need and get on with life. While it does have more details than Jech, I like Jech's style better and not just because it is shorter. (The 2e is just a corrected reprint of 1e.)
Excellent as a follow-up to Kunen Jan 24, 2005
I'm a graduate student in set theory and I'm finding Kanamori an excellent follow-up to Kunen. The book manages to combine detailed technical exposition with historical insight which is actually useful to understanding the material (not just a list of dates) and gives one a "feel" for the subject.
Occasional excersises are contained which are good to help check if you're keeping up (though sometimes the hints are a little too complete: it might be better if these were relegated to an appendix). More exercises would have improved this book.
I believe this is pretty much the only book in which much of this material is collected together, so it's pretty much essential to any-one seriously interested in Set Theory. I await the promised second and third volumes with anticipation!
New edition available Mar 31, 2003
A new edition of this book is available from Springer now, for a lower list price (and one third off if you have ever published in a Springer publication, like LNCS, LNM etc.).