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

Autorentext
Edward B. Saff received his B.S. in mathematics from the Georgia Institute of Technology and his Ph.D. from the University of Maryland, where he was a student of the renowned analyst Joseph L. Walsh. Saff's research areas include approximation theory, numerical analysis, and potential theory. He has published more than 290 mathematical research articles, co-authored 9 books, and co-edited 11 volumes. Recognitions of his research include his election as a SIAM Fellow (Society for Industrial and Applied Mathematics) in 2023, as a Foreign Member of the Bulgarian Academy of Sciences in 2013, as a Fellow of the American Mathematical Society in 2013, as well as a Guggenheim Fellowship in 1978. Saff is co-Editor-in-Chief and Managing Editor of the research journal Constructive Approximation and serves on the editorial boards of Computational Methods and Function Theory and the Journal of Approximation Theory. He has mentored 18 Ph.D.'s as well as 13 post-docs. Saff is currently Distinguished Professor of Mathematics at Vanderbilt University.Vilmos Totik was educated in Hungary and was a professor of mathematics at the University of Szeged and the University of South Florida until his retirement. His main research interest is classical mathematical analysis, approximation theory, orthogonal polynomials and potential theory. He has published (partially with co-authors) 5 monographs, one problem book in set theory and about 220 research papers in various disciplines.

Inhalt
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 [?]^