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Set theory. 2nd, corr. ed. (English) Zbl 0882.03045
Perspectives in Mathematical Logic. Berlin: Springer. xiv, 634 p. (1997).
A very apt review of Jech’s classic text Set Theory appears in an advertisement on page 34 of the Springer Newsletter: Mathematics (1997) Volume 2. The last sentence reads: “The author’s presentation is very well organized, carefully worked out and will become a standard reference.” This was undoubtedly written nearly twenty years ago when the text was first published by Academic Press (1978; [Zbl 0419.03028]).
I am happy to report that indeed the text has become a standard reference, and remains very well organized and carefully worked out. No doubt it will remain a standard reference from which to learn the material that should be part of every set theorist’s general knowledge, and will remain for years to come one of the preferred gateways towards specialized set theory. The first edition of the text had a relatively small number of misprints. The main addition to the second edition is a list of these misprints, given in the back of the book.

MSC:
03Exx Set theory
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
03E05 Other combinatorial set theory
03E45 Inner models, including constructibility, ordinal definability, and core models
03E15 Descriptive set theory
03E40 Other aspects of forcing and Boolean-valued models
03E50 Continuum hypothesis and Martin’s axiom
03E55 Large cardinals
03E35 Consistency and independence results
03E60 Determinacy principles
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