This work is a sequel to the author's G�del's Incompleteness Theorems, though it can be read independently by anyone familiar with G�del'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.
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"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.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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double universality, recursive pairing functions, completely productive function, consistent axiomatizable system, generative relative, recursive superset, double recursion theorem, consistent axiomatizable extension, effective inseparability, uniform reducibility, recursive inseparability, refutable formulas, double analogue, iteration theorem, recursion property, generative set, recursive enumerability, provable formulas, recursive sets, disjoint pair, enumeration theorem, recursion theorems, double productivity, fixed point property, undecidable sentence Key Phrases - Capitalized Phrases (CAPs): (learn more)
Peano Arithmetic, Complete Effective Inseparability, Some Basic Closure Properties, Further Topics, Uniform Gödelization, Shepherdson's Theorems, Proof of Lemma, Weak Recursion Theorems, Pseudo-uniform Reducibility, Metamathematical Applications, Three Special Topics, Double Generativity Browse Sample Pages:
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double universality, recursive pairing functions, completely productive function, consistent axiomatizable system, generative relative, recursive superset, double recursion theorem, consistent axiomatizable extension, effective inseparability, uniform reducibility, recursive inseparability, refutable formulas, double analogue, iteration theorem, recursion property, generative set, recursive enumerability, provable formulas, recursive sets, disjoint pair, enumeration theorem, recursion theorems, double productivity, fixed point property, undecidable sentence Key Phrases - Capitalized Phrases (CAPs): (learn more)
Peano Arithmetic, Complete Effective Inseparability, Some Basic Closure Properties, Further Topics, Uniform Gödelization, Shepherdson's Theorems, Proof of Lemma, Weak Recursion Theorems, Pseudo-uniform Reducibility, Metamathematical Applications, Three Special Topics, Double Generativity Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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3
books
cite this book:
- Logic of Arithmetic (Lectures on Mathematical Logic) by Walter Felscher on page 57, and page 164
- Introduction to Mathematical Logic, Fourth Edition by E. Mendelson in Back Matter
- The Riddle of Scheherazade: And Other Amazing Puzzles by Raymond Smullyan in Front Matter
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