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Computability and Logic Paperback – Sep 17 2007
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"John P. Burgess (Princeton U.) and Richard C. Jeffrey continue here in the tradition set by the late Boolos to present the "principal fundamental theoretical results logic" that would necessarily include the work of G<:o>del. For this edition they have revised and simplified their presentation of the representability of recursive functions, rewritten a section on Robinson arithmetic, and reworked exercises. They continue to present material in a two-semester format, the first on computability theory (enumerability, diagonalization, Turing compatibility, uncomputability, abacus computability, recursive functions, recursive sets and relations, equivalent definitions of computability) and basic metalogic (syntax, semantics, the undecidability of first-order logic, models and their existence, proofs and completeness, arithmetization, representability of recursive functions, indefinability, undecidability, incompleteness and the unprobability of inconsistency). They include a slate of nine further topics, including normal forms, second-order logic and Ramsey's theorem."
Book News, Inc.
Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem.
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Most Helpful Customer Reviews on Amazon.com (beta)
As far as approach is concerned, the book places recursion theory at the center. The first several chapters introduce the basics of this subject, and only then do the authors turn toward theories of arithmetic and the like. This corresponds to what is probably the dominant way of thinking of Goedel's theorem: that, at its core, it is a theorem in recursion theory.
Other topics are covered along the way, too, of course, and there are several different courses one could teach using this book. The selection of problems is good, too.
Do you understand why a logical system that proves its own consistency must be inconsistent? If not, and you think this is an interesting question, this is the book for you.
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