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A Course in Mathematical Logic for Mathematicians (Hardcover, 2nd ed. 2010)
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A Course in Mathematical Logic for Mathematicians (Hardcover, 2nd ed. 2010)
Series: Graduate Texts in Mathematics, 53
Expected to ship within 10 - 15 working days
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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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