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A Course in Mathematical Logic for Mathematicians

Springer New York,
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This fresh edition of the straightforward introduction to modern mathematical logic retains its appeal to the intuition of working mathematicians, yet along with the material from the first edition, it has fresh chapters, one of which deals with Model Theory.

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Titel: A Course in Mathematical Logic for Mathematicians
Autoren/Herausgeber: Yu. I. Manin
Übersetzer: Neal Koblitz
Weitere Mitwirkende: B. Zilber
Aus der Reihe: Graduate Texts in Mathematics
Ausgabe: 2nd ed. 2010

ISBN/EAN: 9781441906144

Seitenzahl: 384
Format: 23,5 x 15,5 cm
Produktform: Hardcover/Gebunden
Gewicht: 1,640 g
Sprache: Englisch

1. The ?rst edition of this book was published in 1977. The text has been well received and is still used, although it has been out of print for some time. In the intervening three decades, a lot of interesting things have happened to mathematical logic: (i) Model theory has shown that insights acquired in the study of formal languages could be used fruitfully in solving old problems of conventional mathematics. (ii) Mathematics has been and is moving with growing acceleration from the set-theoretic language of structures to the language and intuition of (higher) categories, leaving behind old concerns about in?nities: a new view of foundations is now emerging. (iii) Computer science, a no-nonsense child of the abstract computability theory, has been creatively dealing with old challenges and providing new ones, such as the P/NP problem. Planning additional chapters for this second edition, I have decided to focus onmodeltheory,the conspicuousabsenceofwhichinthe ?rsteditionwasnoted in several reviews, and the theory of computation, including its categorical and quantum aspects. The whole Part IV: Model Theory, is new. I am very grateful to Boris I. Zilber, who kindly agreed to write it. It may be read directly after Chapter II. The contents of the ?rst edition are basically reproduced here as Chapters I–VIII. Section IV.7, on the cardinality of the continuum, is completed by Section IV.7.3, discussing H. Woodin’s discovery.

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