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Set theory. Transl. from the Hungarian by Attila Máté. (English) Zbl 0934.03057

London Mathematical Society Student Texts. 48. Cambridge: Cambridge University Press. viii, 316 p. (1999).
This book consists of two parts and an Appendix to Part I. The first part contains a general introduction to classical set theory, including: cardinal and ordinal numbers; transfinite induction and recursion; some consequences of the Axiom of Choice; elements of cardinal arithmetic; the Continuum Hypothesis CH and the Generalized Continuum Hypothesis GCH. The Appendix attached to Part I gives more details about axiomatic set theory. In particular, the ZFC axiom system is introduced and the precise notion of independence proofs in set theory is discussed. The second part contains an excellent course of combinatorial set theory, including: the theory of stationary sets; \(\Delta\)-systems; partition relations and Ramsey’s theorem; measurable, real measurable and inaccessible cardinals. The two final sections give an introduction to the modern theory of singular cardinals with some deep results of S. Shelah. A large number of interesting problems are given after each section. Hints to more difficult problems (and the references to the literature) are included at the end of each part.

MSC:

03Exx Set theory
03-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations
03E05 Other combinatorial set theory
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
03E20 Other classical set theory (including functions, relations, and set algebra)
03E30 Axiomatics of classical set theory and its fragments
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