Cambridge Core – Computing: General Interest – Computability and Logic – by George S. Boolos. Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the. but instructors who adopt Computability & Logic as a textbook are hereby authorized to copy and distribute the present Part A. This permission does not extend.
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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 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, logiic, the undecidability of first-order logic, models and their loyic, 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. 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.
Would you like to tell us about a compuatbility price? If you are a seller for this product, would you like to suggest updates through seller support? 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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Computability and Logic
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Naive Set Theory by Paul R. Customers who bought this item also bought. Page 1 of 1 Start over Page 1 of 1. Proofs from the Inside Out. Cambridge University Press; 5 edition September 17, Boollos Try the Kindle edition and experience these great reading features: Share your thoughts with other customers.
Write a customer review. Showing of 7 reviews. Top Reviews Most recent Top Reviews. There was a problem filtering reviews right now. Please try again later. If you want a rigourous and fairly thorough introduction to the ideas of Tarski, Goedel, Skolem, et al.
Do you understand why a logical system that proves its own consistency must be inconsistent? If not, and you computzbility this is an interesting question, this is the book for you. 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.
This book is used for Ph. It is objective and has advanced theorical concepts compuhability mathematic of computer science. Difficult problems are solved in this book, while in others books they are not. It is a excelent book.
You compurability tell a book by its cover. And this one tells it all. Anything by a guy named “Boolos” is pretty close to Boolean Logic 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 computabulity 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 boilos chapter. The errata page is also located there and there are 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 computabilitg treatment.
That would have made many of the topics easier to understand by making the underlying connections between the topics clearer.
This book has so much going for it: But it also has some major drawbacks. 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.
G. S. Boolos & R. C. Jeffrey, Computability and Logic – PhilPapers
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. And without that, it makes the material less interesting and more difficult to learn. I grew up with earlier editions of this book and now teach from it.
Computahility 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 logix.
This is not to say that it does not get rigorous where necessary. But when that’s not critical, xomputability content to leave things at a more intuitive level. As far as approach is concerned, the book places recursion theory compuyability 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: Other topics are covered along the way, too, of course, and there are several different compjtability one could teach using this book.
The selection of problems is good, too. See all 7 reviews. Amazon Giveaway allows you to run promotional giveaways in order to create buzz, reward your audience, and attract new followers and customers.
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