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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