Cambridge Introductions to Philosophy Ser.: An Introduction to Gödel's Theorems by Peter Smith (2013, Trade Paperback, Revised edition)

Cambridge University Press

1107606756

9781107606753

164720077

Peter Smith

Introduction to Gödel's Theorems

Trade Paperback

English

Revised

2013

Cambridge Introductions to Philosophy Ser.

Textbook

402 Pages

9.7in

0.7in

6.9in

27.9 Oz

Qa9.65 .S65 2013

Revised Edition

2

"Smith breathes new life into the work of Kurt Godel in this second edition ... Recommended. Upper-division undergraduates through professionals." R. L. Pour, Choice

Preface; 1. What Gödel's theorems say; 2. Functions and enumerations; 3. Effective computability; 4. Effectively axiomatized theories; 5. Capturing numerical properties; 6. The truths of arithmetic; 7. Sufficiently strong arithmetics; 8. Interlude: taking stock; 9. Induction; 10. Two formalized arithmetics; 11. What Q can prove; 12. Io, an arithmetic with induction; 13. First-order Peano arithmetic; 14. Primitive recursive functions; 15. LA can express every p.r. function; 16. Capturing functions; 17. Q is p.r. adequate; 18. Interlude: a very little about Principia; 19. The arithmetization of syntax; 20. Arithmetization in more detail; 21. PA is incomplete; 22. Gödel's First Theorem; 23. Interlude: about the First Theorem; 24. The Diagonalization Lemma; 25. Rosser's proof; 26. Broadening the scope; 27. Tarski's Theorem; 28. Speed-up; 29. Second-order arithmetics; 30. Interlude: incompleteness and Isaacson's thesis; 31. Gödel's Second Theorem for PA; 32. On the 'unprovability of consistency'; 33. Generalizing the Second Theorem; 34. Löb's Theorem and other matters; 35. Deriving the derivability conditions; 36. 'The best and most general version'; 37. Interlude: the Second Theorem, Hilbert, minds and machines; 38. -Recursive functions; 39. Q is recursively adequate; 40. Undecidability and incompleteness; 41. Turing machines; 42. Turing machines and recursiveness; 43. Halting and incompleteness; 44. The Church-Turing thesis; 45. Proving the thesis?; 46. Looking back.

2013

Scholarly & Professional

Logic, Science & Technology

2012-554703

511.3

22

Yes

Biography & Autobiography, Mathematics