Problems and Theorems in Classical Set Theory

This is the first comprehensive collection of problems in set theory. It contains well chosen sequences of exercises. Most of the problems are challenging and require work, wit, and inspiration. The book is destined to become a classic.

This is the first comprehensive collection of problems in set theory. But rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution. This is destined to become a classic, and will be an important resource for students and researchers. It follows a tradition of Hungarian mathematics started with Pólya-Szegõ's problem book in analysis and continued with Lovász' problem book in combinatorics.

Well chosen sequences of exercises leading to the proofs of basic results of different special topics Collects the classical results of set theory as developed after the discovery of modern axiomatic methods

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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 1920-1970. 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 Pólya-Szegõ's problem book in analysis and continued withLovász' 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.

Contenu
Problems.- Operations on sets.- Countability.- Equivalence.- Continuum.- Sets of reals and real functions.- Ordered sets.- Order types.- Ordinals.- Ordinal arithmetic.- Cardinals.- Partially ordered sets.- Transfinite enumeration.- Euclidean spaces.- Zorn's lemma.- Hamel bases.- The continuum hypothesis.- Ultrafilters on ?.- Families of sets.- The Banach-Tarski paradox.- Stationary sets in ?1.- Stationary sets in larger cardinals.- Canonical functions.- Infinite graphs.- Partition relations.- ?-systems.- Set mappings.- Trees.- The measure problem.- Stationary sets in [?]^- The Banach-Tarski paradox.- Stationary sets in ?1.- Stationary sets in larger cardinals.- Canonical functions.- Infinite graphs.- Partition relations.- ?-systems.- Set mappings.- Trees.- The measure problem.- Stationary sets in [?]^