Introduction to Goedel''s Theorems

Informationen zum Autor Peter Smith was formerly Senior Lecturer in Philosophy at the University of Cambridge. His books include Explaining Chaos (1998) and An Introduction to Formal Logic (2003) and he is also a former editor of the journal Analysis. Klappentext A clear and accessible treatment of Godel's famous! intriguing! but much misunderstood incompleteness theorems! extensively revised in a second edition. Zusammenfassung An extensively rewritten second edition of this best-selling standard text for graduates and upper-level undergraduate students of logic! philosophy of mathematics! and pure mathematics. A clear and accessible treatment of Goedel's famous! intriguing! but much misunderstood incompleteness theorems. Inhaltsverzeichnis Preface; 1. What Godel'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. Godel'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. Godel'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. mu-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. ...

Détails du produit

• Auteurs: Peter Smith
• Edition: Cambridge University Press ELT
• Langues: Anglais
• Format d'édition: Livre Relié
• Sortie: 21.02.2013
• EAN: 9781107022843
• ISBN: 978-1-107-02284-3
• Pages: 406
• Thèmes: Cambridge Introductions to Phi; Cambridge Introductions to Phi
• Catégories: Sciences humaines, art, musique > Philosophie > Général, dictionnaires; Sciences naturelles, médecine, informatique, technique > Mathématiques > Général, dictionnaires