Introduction to set theory. The set theory of Georg Cantor and its axiomatization by Ernst Zermelo. 2., verbesserte und erw. Aufl. (Einführung in die Mengenlehre. Die Mengenlehre Georg Cantors und ihre Axiomatisierung durch Ernst Zermelo.) (German) Zbl 1042.03001
Springer-Lehrbuch. Berlin: Springer (ISBN 3-540-20401-6/pbk). 551 S. (2004).
The second edition of the book is a revised and enlarged version of the first edition [Berlin: Springer (2002; Zbl 0988.03004)]. So the number of pages increased from 330 pages to 550 pages. In the following we describe the relevant changes.
The author deals with various definitions of infinity. He has included a chapter on cardinal arithmetic. In great detail he describes antinomies in set theory. He defines the Borel-Hausdorff hierarchy and has added a chapter on cofinalities, filters and large cardinals. He deals with stationary sets, proves Fodor’s lemma and uses Ulam matrices for the construction of pairwise disjoint stationary sets. Further on he describes the Hausdorff residue.
He discusses axiomatizations for a set theory with classes and he has added a biography of Felix Hausdorff.
The author deals with various definitions of infinity. He has included a chapter on cardinal arithmetic. In great detail he describes antinomies in set theory. He defines the Borel-Hausdorff hierarchy and has added a chapter on cofinalities, filters and large cardinals. He deals with stationary sets, proves Fodor’s lemma and uses Ulam matrices for the construction of pairwise disjoint stationary sets. Further on he describes the Hausdorff residue.
He discusses axiomatizations for a set theory with classes and he has added a biography of Felix Hausdorff.
Reviewer: Martin Weese (Potsdam)
MSC:
| 03-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations |
| 03E10 | Ordinal and cardinal numbers |
| 03-03 | History of mathematical logic and foundations |
| 01A55 | History of mathematics in the 19th century |
| 01A60 | History of mathematics in the 20th century |
