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Computability and Logic [Paperback]

George S. Boolos , John P. Burgess , Richard C. Jeffrey

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Book Description

Sept. 17 2007 0521701465 978-0521701464 5
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. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a new and simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems.

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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.

Book Description

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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Amazon.com: 4.3 out of 5 stars  7 reviews
26 of 28 people found the following review helpful
3.0 out of 5 stars Could be much better March 21 2009
By Pedestrian - Published on Amazon.com
Format:Paperback
This book has so much going for it: eminent authors, great coverage, lots of exercises and it's quite inexpensive for a math book. But it also has some major drawbacks. First of all: the typos. Oh the typos. I've seen reviews for the fourth edition where there were lots of complaints about the typos. This (the fifth edition) may be an improvement but there are still way too many typos. A bigger problem is that the authors don't always make the important conceptual connections between the material explicit - and this may be the result of a book written by committee. To give an example, there is a whole chapter on enumerability with no mention of decidability. When the authors finally introduce decidability sixty pages later it is not clearly compared with enumerability. But these concepts are related in a very simple but important way - something a beginning student would not realize on reading this book. Finally, the authors don't do a good job of presenting the *big picture* in mathematical logic. And without that, it makes the material less interesting and more difficult to learn.
9 of 9 people found the following review helpful
4.0 out of 5 stars Pretty good intermediate textbook on logic and topics in the foundations of mathematics. Oct. 13 2010
By Nan Chen - Published on Amazon.com
Format:Paperback
This is quite good but the book quickly dives into intermediate or advanced topics in mathematical logic, recursion theory (aka computability) and set theory. Many topics are covered (one of the strengths of the book). The exercises are good, interesting, helpful and can be challenging which is why if you're a novice studying logic it's probably better to start off with a more elementary text focusing on 1st order logic deductions and some of the meta-theoretic results (completeness, soundness, etc) before tackling this textbook. The exercises are an improvement in my opinion, from earlier editions of the book. Many of the answers can be found on the website given in the introductory chapter. The errata page is also located there (and there's plenty of errata to be found in this book, unfortunately!). It also seems that many of the chapters could have been combined and given more of a holistic treatment. That would have made many of the topics easier to understand by making the underlying connections between the topics clearer.
11 of 12 people found the following review helpful
4.0 out of 5 stars Very good textbook Oct. 10 2009
By Richard G. Heck - Published on Amazon.com
Format:Kindle Edition
I grew up with earlier editions of this book and now teach from it. It's an excellent introduction to this material, pitched at just the right level, in my experience, for its intended audience. For students (or people in general) who are extremely sophisticated mathematically, it can sometimes seem a little unrigorous. But for my students, who are mostly philosophers, it manages to convey a sense for what is going on without overdoing it on the detail. This is not to say that it does not get rigorous where necessary. It does. But when that's not critical, it's content to leave things at a more intuitive level.

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.
5 of 6 people found the following review helpful
4.0 out of 5 stars Worked for class Feb. 25 2010
By Rare Reviewer - Published on Amazon.com
Format:Paperback|Verified Purchase
My professor uses this book to the last word. It's a good book overall however the content is not exactly easy. I would recommend this for someone who has a little knowledge of the subject. A novice could possibly use it with the help of google.
2 of 3 people found the following review helpful
5.0 out of 5 stars Brilliant and Authoritative March 2 2013
By Herbert Gintis - Published on Amazon.com
Format:Paperback|Verified Purchase
If you want a rigourous and fairly thorough introduction to the ideas of Tarski, Goedel, Skolem, et al., and you never really understood the Loewenheim-Skolem theorem or Tarski theory of truth, this is the book for you.
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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