Computability and Logic - Brossura

Boolos, George S.; Jeffrey, Richard C.

Brossura

ISBN 10: 0521389232 ISBN 13: 9780521389235

Casa editrice: Cambridge University Press, 1989

Riassunto

A text for a second course in logic for graduate and advanced undergraduate students. This third edition has been corrected and contains thoroughly revised versions of the chapters on Ramsey and provability, with new exercises provided for three other chapters. There are also two new chapters dealing with undecidable sentences and on the non-existence of non-standard recursive models of Z.

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Recensione

‘Intended for a second course in logic it gives excellent coverage of the fundamental theoretical results about logic involving computability, undecidability, axiomatization, definability, incompleteness, etc.’ American Math Monthly

‘... particularly appropriate for graduate and advanced undergraduate students in philosophy ... The book is written in a clear and pleasing style and avoids pedantry ... It should be an excellent text for its intended audience.’ Mathematical Reviews

Contenuti

Preface; Preface to the third edition; 1. Enumerability; 2. Diagonalization; 3. Turing machines; 4. Uncomputability via the busy beaver problem; 5. Uncomputability via diagonalization; 6. Abacus computable functions are Turing computable; 7. Recursive functions are abacus computable; 8. Turing computable functions are recursive; 9. First-order logic revisited; 10. First-order logic is undecidable; 11. First-order logic formalized: derivations and soundness; 12. Completeness of the formalization: compactness; 13. The Skolem-Löwenheim theorem; 14. Representability in Q; 15. Undecidability, indefinability and incompleteness; 16. Provability predicates and the unprovability of consistency; 17. Non-standard models of arithmetic; 18. Second-order logic; 19. On defining arithmetical truth; 20. Definability arithmetic and forcing; 21. The decidability of arithmetic with addition, but not multiplication; 22. Dynadic logic is undecidable: ‘eliminating’ names and function symbols; 23. The Craig interpolation lemma; 24. Two applications of Craig‘s lemma; 25. Monadic versus dyadic logic; 26. Ramsey’s theorem; 27. Provability considered modal-logically; 28. Undecidable sentences; 29. Non-standard models of Z are not recursive; Index.

Dettagli dell?edizione

• Editore: Cambridge University Press
• Data di pubblicazione: 1989
• ISBN 10: 0521389232
• ISBN 13: 9780521389235
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero edizione: 3
• Numero di pagine: 320