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An Introduction to Gödel's Theorems (Cambridge Introductions to Philosophy)
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Located in: Springfield, Oregon, United States
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eBay item number:226160634825
Item specifics
- Condition
- Release Year
- 2013
- Book Title
- An Introduction to Gödel's Theorems (Cambridge Introductions ...
- Subject
- Logic, Science & Technology
- ISBN
- 9781107606753
- Subject Area
- Biography & Autobiography, Mathematics
- Publication Name
- Introduction to Gödel's Theorems
- Publisher
- Cambridge University Press
- Item Length
- 9.7 in
- Publication Year
- 2013
- Series
- Cambridge Introductions to Philosophy Ser.
- Type
- Textbook
- Format
- Trade Paperback
- Language
- English
- Item Height
- 0.7 in
- Features
- Revised
- Item Weight
- 27.9 Oz
- Item Width
- 6.9 in
- Number of Pages
- 402 Pages
About this product
Product Information
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.
Product Identifiers
Publisher
Cambridge University Press
ISBN-10
1107606756
ISBN-13
9781107606753
eBay Product ID (ePID)
164720077
Product Key Features
Number of Pages
402 Pages
Language
English
Publication Name
Introduction to Gödel's Theorems
Publication Year
2013
Subject
Logic, Science & Technology
Features
Revised
Type
Textbook
Subject Area
Biography & Autobiography, Mathematics
Series
Cambridge Introductions to Philosophy Ser.
Format
Trade Paperback
Dimensions
Item Height
0.7 in
Item Weight
27.9 Oz
Item Length
9.7 in
Item Width
6.9 in
Additional Product Features
Edition Number
2
Intended Audience
Scholarly & Professional
LCCN
2012-554703
Dewey Edition
22
Reviews
"Smith breathes new life into the work of Kurt Godel in this second edition ... Recommended. Upper-division undergraduates through professionals." R. L. Pour, Choice
Illustrated
Yes
Dewey Decimal
511.3
Edition Description
Revised Edition
Lc Classification Number
Qa9.65 .S65 2013
Table of Content
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.
Copyright Date
2013
Item description from the seller
Seller assumes all responsibility for this listing.
eBay item number:226160634825
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Springfield, Oregon, United States
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