An introduction to godel's theorems
Series: Cambridge introductions to philosophyPublication details: 2013 New York Cambridge University PressEdition: 2nd edDescription: xvi, 388 pISBN:- 9781107606753
- 511.3 S6I6
| Item type | Current library | Item location | Collection | Shelving location | Call number | Status | Date due | Barcode | |
|---|---|---|---|---|---|---|---|---|---|
| Books | Vikram Sarabhai Library | Rack 28-A / Slot 1354 (0 Floor, East Wing) | Non-fiction | General Stacks | 511.3 S6I6 (Browse shelf(Opens below)) | Available | 191973 |
Table of Contents
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. I∆o, 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. Lob’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. μ-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
In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book – extensively rewritten for its second edition – will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.
(http://www.cambridge.org/us/academic/subjects/philosophy/logic/introduction-godels-theorems-2nd-edition)
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