ISBN-10:
0521674530
ISBN-13:
2900521674538
Pub. Date:
07/31/2007
Publisher:
Cambridge University Press
Introduction to Gödel's Theorems / Edition 1

Introduction to Gödel's Theorems / Edition 1

by Peter Smith

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Product Details

ISBN-13: 2900521674538
Publisher: Cambridge University Press
Publication date: 07/31/2007
Series: Cambridge Introductions to Philosophy Series
Edition description: New Edition
Pages: 376
Product dimensions: 6.00(w) x 1.25(h) x 9.00(d)

About the Author

Peter Smith is Lecturer in Philosophy at the University of Cambridge. His books include Explaining Chaos (1998) and An Introduction to Formal Logic (2003), and he is a former editor of the journal Analysis.

Table of Contents

Preface; 1. What Gödel's Theorems say; 2. Decidability and enumerability; 3. Axiomatized formal theories; 4. Capturing numerical properties; 5. The truths of arithmetic; 6. Sufficiently strong arithmetics; 7. Interlude: taking stock; 8. Two formalized arithmetics; 9. What Q can prove; 10. First-order Peano Arithmetic; 11. Primitive recursive functions; 12. Capturing funtions; 13. Q is p.r. adequate; 14. Interlude: a very little about Principia; 15. The arithmetization of syntax; 16. PA is incomplete; 17. Gödel's First Theorem; 18. Interlude: about the First Theorem; 19. Strengthening the First Theorem; 20. The Diagonalization Lemma; 21. Using the Diagonalization Lemma; 22. Second-order arithmetics; 23. Interlude: incompleteness and Isaacson's conjecture; 24. Gödel's Second Theorem for PA; 25. The derivability conditions; 26. Deriving the derivability conditions; 27. Reflections; 28. Interlude: about the Second Theorem; 29. Recursive functions; 30. Undecidability and incompleteness; 31. Turing machines; 32. Turing machines and recursiveness; 33. Halting problems; 34. The Church-Turing Thesis; 35. Proving the Thesis?; 36. Looking back.

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