About this product

Product Identifiers

PublisherOxford University Press, Incorporated

ISBN-10019508232X

ISBN-139780195082326

eBay Product ID (ePID)24038255960

Product Key Features

Number of Pages184 Pages

Publication NameRecursion Theory for Metamathematics

LanguageEnglish

SubjectLogic

Publication Year1993

TypeTextbook

Subject AreaMathematics

AuthorRaymond M. Smullyan

SeriesOxford Logic Guides

FormatHardcover

Dimensions

Item Height0.8 in

Item Weight14.5 Oz

Item Length9.3 in

Item Width6.2 in

Additional Product Features

Intended AudienceCollege Audience

LCCN92-040495

Dewey Edition20

Reviews". . . 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." --RomanMurawski, Mathematical 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, "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, "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, "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, "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, "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 tometamathematics. 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"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 tometamathematics. 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, "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 thework 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

Series Volume Number22

IllustratedYes

Dewey Decimal511.35

Table Of Content1. Recursive Enumerability and Recursivity2. Undecidability and Recursive Inseparability3. Indexing4. Generative Sets and Creative Systems5. Double Generativity and Complete Effective Inseparability6. Universal and Doubly Universal Systems7. Shepherdson Revisited8. Recursion Theorems9. Symmetric and Double Recursion Theorems10. Productivity and Double Productivity11. Three Special Topics12. Uniform Godelization

SynopsisThis work is a sequel to the author's Godel's Incompleteness Theorems, though it can be read independently by anyone familiar with Godel'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., 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., In 1931, Princeton mathematician Kurt Gödel startled the scientific world with his Theorem of Undecidability, which showed that some statements in mathematics are inherently 'undecidable'. This volume of the Oxford Logic Guides is a sequel to Smullyan's Gödel's Incompleteness Theorems (Oxford Logic Guides No. 19, 1992), but it can be read independently by anyone familiar with at least one proof of Gödel's incompleteness theorem for Peano Arithmetic. This volume was written for mathematicians, philosphers, and computer scientists who are curious about Gödel's incompleteness theorems. The only prerequisite would be a first course in mathematical logic.

LC Classification NumberQA9.6.S68 1993