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Recursion Theory for Metamathematics (Oxford Logic Guides) [Hardcover]

Raymond M. Smullyan
5.0 out of 5 stars  See all reviews (2 customer reviews)

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Book Description

January 28, 1993 019508232X 978-0195082326 First Printing
This work is a sequel to the author's Gödel's Incompleteness Theorems, though it can be read independently by anyone familiar with Gödel's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.

Editorial Reviews


"A self-contained exposition, it presumes neither a reading of the previous volume . . . nor a prior knowledge of recursion theory. The reader with some familiarity with both recursion theory and logic should find this an excellent source for the interconnections between them." --Choice

"Smullyan is not only an outstanding authority on this subject, but is also a skilled pedagogue, with a special talent for formulating simple riddles, which illuminate this very difficult and profound subject. Smullyan has made an important contribution toward the wider understanding of the work of Godel and his followers. . . . Smullyan plays a significant role in the further development of mathematical logic and the elucidation of its relation to metamathematics. He continues to be one of the foremost popularizers of the subject." --American Scientist

". . . an interesting presentation of recursion theory from the point of view of its applications in metamathematics, indicating many interrelations between various notions and properties. It will certainly be studied carefully and referred to by students and specialists alike." --Roman Murawski, Mathematical Reviews

About the Author

Raymond M. Smullyan is at Indiana University.

Product Details

  • Series: Oxford Logic Guides (Book 22)
  • Hardcover: 184 pages
  • Publisher: Oxford University Press; First Printing edition (January 28, 1993)
  • Language: English
  • ISBN-10: 019508232X
  • ISBN-13: 978-0195082326
  • Product Dimensions: 9.2 x 6.1 x 0.4 inches
  • Shipping Weight: 15.2 ounces (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #1,364,869 in Books (See Top 100 in Books)

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0 of 1 people found the following review helpful
5.0 out of 5 stars Price Update November 1, 2013
Format:Hardcover|Verified Purchase
With due respect for other reviewers, services like half (an ebay service) and a few other sellers are now offering used versions of this classic for about $40. New prices are more than on Amazon. ALL those sellers have the same titles here on Amazon (see the used third parties) for the same or less.

But that begs the question: do you even WANT to pay $40 (or even $20 US) for this book? Recursion, as a subject, goes from relatively simple (Russian dolls and fractals) to extremely complex (Computer Science and numeric analysis techniques, Godel, as this text, etc). This classic work is MORE advanced than the author's original Godel (Godel's Incompleteness Theorems (Oxford Logic Guides)) text, and requires grad level math to appreciate.

In fact, recursion (essentially self similarity) also is even being written about as the essence of self awareness, and even the basis of thinking itself (see the recursive mind-- The Recursive Mind: The Origins of Human Language, Thought, and Civilization-- an amazing book on many aspects of recursion).

This is a small book, and is not nearly as simple as numerous "layman" versions of Godel, yet not as complex as the Dover classic editions you can get for $8 US if you REALLY get the math and want to go deep. Put recursion in Amazon's search, you'll find a wealth of other options.
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7 of 29 people found the following review helpful
5.0 out of 5 stars guess what? July 18, 2001
By A Customer
you can buy this for less than twenty bucks on's website
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