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Theory of Recursive Functions and Effective Computability Paperback – April 22, 1987

4.5 out of 5 stars 10 customer reviews

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Product Details

  • Paperback: 506 pages
  • Publisher: The MIT Press (April 22, 1987)
  • Language: English
  • ISBN-10: 0262680521
  • ISBN-13: 978-0262680523
  • Product Dimensions: 6 x 1 x 9 inches
  • Shipping Weight: 1.7 pounds (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon Best Sellers Rank: #1,333,249 in Books (See Top 100 in Books)

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Top Customer Reviews

Format: Paperback
I looked long and hard for a reference in recursion theory and this was the only one which was acceptable. Luckily it is also quite good.
Most books in the subject either introduce the material in their own non-standard notation which, while suitable for a survey course in the material is of little help when attempting to actually read papers in the field. These books are also usually very basic ignoring things like the arithmetical hierarchy. Other books in this subject seem to mostly be advanced texts and don't cover, or cover very briefly, the important theorems.
This book starts at turing machines and recursive functions. Going through the basic results like the halting problem and rapidly moving on to more advanced topics like creative sets, cylinders and hypersimple sets. Posts problem(with Friedberg's solution) and the fixed point theorem are covered as well. The final part of the book covers degrees of unsolvability arithmetical hierarchy and the analytic hierarchy.
While the book does cover recursive fucntions and turing machines I would suggest previous experience with them before reading as the coverage is brief and doesn't give the reader a feeling of how these systems work.
If you are taking a class in the subject or want to understand modern recursion theory this is a wonderful place to start.
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By A Customer on June 21, 2003
Format: Paperback
There are a lot of good introductory books on computation theory,
but after reading them you may be left asking "okay, what do
I read next?" Well _this_ is the book. If you're looking for something in between the undergraduate intro books and
the research-level articles then this is for you. It develops recursive function theory in a succinct, mathematically mature manner that is freed from the details of any particular formalism. You should have previous exposure to turing machines and undecidable problems, an appreciation of the defense and use of Church's thesis, and familiarity with basic mathematical logic. Just to be clear, this book is NOT:
-a computer science, programming, or algorithms book
-an introductory book
-a book about automata or weak models of computation (such as regular languages or context-free grammars)
-a complexity theory book (no time bounds or np-completeness etc)
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By Todd Ebert on September 14, 2000
Format: Paperback
The definitive book on computabilty and recursive function theory. I remember reading this book in preparation for research in complexity theory. I found it very stressful reading the book, but it was a good kind of stress. The kind that forces you to think deeply about what the author is writing about. In addition to the main text, the author provides numerous thought-provoking problems whose study could make a coure unto themselves. I read this book as a 3rd-year graduate student in
math. If you are an undergraduate and are interested in computability theory, I recommend Nigel's Cutland's book on the subject.
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Format: Paperback
If there's a better book on recursive function theory, I havent seen it. It's wonderfully well-written, extremely interesting, and good both for learning and quick reference. There are lots of neat exercises- this book will keep you busy for a long time. If you are interested in recursive function theory you must have this book- I dont need to say anything else.
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Format: Paperback
After four decades, this is still the most popular graduate text on recursion theory. I think the success is due to its stock of valuable material rather than the quality of writing. The style is dense, descriptions are overly brief, and explanations are poorly laid out. Proofs are brief and sketchy. Overall, it is just poor writing. Take a look at Odifreddi to see recursion theory from someone with a talent for readable prose.

It says no previous logic course is assumed, but you actually need set theory and basic logic from the beginning. Also, coverage of the basics is cursory, so it would help to have done something like Cutland.
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