Computability and Logic 5th Edition by George S. Boolos (PDF)

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. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems. This updated edition is also accompanied by a website as well as an instructor’s manual.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I really liked the style. On one hand, it looks like you are having a chat with the authors, on the other, it is perfectly formal and rigorous. No tedious parts, just pure ideas! And perfect examples!Exercises after each chapter were great, complex problems were divided into a few problems which I really liked. Maybe some of them were trivial but I didn’t mind that. Overall, I think that this is a great text for every math graduate since these subtle ideas are simply skipped in most logic courses. And also this would be of value to a motivated high schooler who is not quite sure what math really is.

⭐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.

⭐no comment

⭐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.D. students of computer science. It is objective and has advanced theorical concepts about mathematic of computer science. Difficult problems are solved in this book, while in others books they are not. It is a excelent book.

⭐You can tell a book by its cover.And this one tells it all.Anything by a guy named “Boolos” ispretty close to Boolean Logic….Isn’t It??

⭐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.

⭐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.

⭐I got this for self study (but have studied the topics in lesser detail while in college, but a long time back), and was confident that I will be able to understand most of it (except the more advanced further topics part). I think the organization of the book and the writing style is amazing, and care has been taken to make sure one does not loose the context or the big picture. Also, in some cases multiple ways of achieving the same result has been shown so readers can appreciate the nature of problem better.But I think the authors could have slowed down the pace of getting into some critical concepts, like minimization, semirecursiveness… also it’s super confusing to see which functions are total and which partial in the recursive functions chapter. Also there are multiple definitions in a single paragraph at many places (in FOL chapters for instance), and its very easy to miss finer points and those parts have to read multiple times. The book is already thin (around 300 pages) so adding in another say 50 pages is not going to be a deal breaker. This is why I take out 1 star from rating. But if someone is using it along with a lecture or as a reference text then they should be fine.In author’s defense I didn’t attempt most of the exercises which now I come to think of it is a must to get most out of such a book. So, if you plan to self study I strongly suggest going through the exercises and just follow the usual reading order (I didn’t find jumping between chapters any useful).

⭐Clear and thorough explanations of concepts that I’ve only seen explained in passing before. I thoroughly recommend this book for people wanting to learn computer science fundamentals.

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