Problems and Theorems in Classical Set Theory
Authors: Komjath, Peter, Totik, Vilmos
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 About this Textbook

This is the first comprehensive collection of problems in set theory. Most of classical set theory is covered, classical in the sense that independence methods are not used, but classical also in the sense that most results come from the period between 19201970. Many problems are also related to other fields of mathematics such as algebra, combinatorics, topology and real analysis. The authors choose not to concentrate on the axiomatic framework, although some aspects are elaborated (axiom of foundation and the axiom of choice). Rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. The problems are organized in a way that earlier problems help in the solution of later ones. For many problems, the authors trace the origin and provide proper references at the end of the solution.
The book follows a tradition of Hungarian mathematics started with PólyaSzegõ's problem book in analysis and continued with Lovász' problem book in combinatorics. This is destined to become a classic, and will be an important resource for students and researchers.
Péter Komjáth is a professor of mathematics at the Eötvös Lóránd University, Budapest. Vilmos Totik is a professor of mathematics at the University of South Florida, Tampa and University of Szeged.
 Reviews

From the reviews:
"The volume contains 1007 problems in (mostly combinatorial) set theory. As indicated by the authors, "most of classical set theory is covered, classical in the sense that independence methods are not used, but classical also in the sense that most results come from the period, say, 19201970. Many problems are also related to other fields of mathematics such as algebra, combinatorics, topology and real analysis." And indeed the topics covered include applications of Zorn's lemma, Euclidean spaces, Hamel bases, the BanachTarski paradox and the measure problem. The statement of the problems, which are distributed among 31 chapters, takes 132 pages, and the (fairly detailed) solutions (together with some references) another 357 pages. Some problems are elementary but most of them are challenging. For example, in Chapter 29 the reader is asked in Problem 1 to show that $[\lambda]^{<\kappa}$ is the union of $\kappa$ bounded sets, and in Problem 20 to prove Baumgartner's result that every closed unbounded subset of $[\omega_2]^{<\aleph_1}$ is of maximal cardinality $\aleph_2^{\aleph_0}$. This is a welcome addition to the literature, which should be useful to students and researchers alike." (Pierre Matet, Mathematical Reviews)
"The book is well written and self contained, a choice collection of hundreds of tastefully selected problems related to classical set theory, a wealth of naturally arising, simply formulated problems … . It is certainly available to students of mathematics major even in their undergraduate years. The solutions contain the right amount of details for the targeted readership. … This is a unique book, an excellent source to review the fundamentals of classical set theory, learn new tricks, discover more and more on the field." (Tamás Erdélyi, Journal of Approximation Theory, 2008)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Problems and Theorems in Classical Set Theory
 Authors

 Peter Komjath
 Vilmos Totik
 Series Title
 Problem Books in Mathematics
 Copyright
 2006
 Publisher
 SpringerVerlag New York
 Copyright Holder
 SpringerVerlag New York
 eBook ISBN
 9780387362199
 DOI
 10.1007/0387362193
 Hardcover ISBN
 9780387302935
 Softcover ISBN
 9781441921406
 Series ISSN
 09413502
 Edition Number
 1
 Number of Pages
 XII, 516
 Topics