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E-raamat: Aspects of Incompleteness

(Göteborgs Universitet, Sweden)
  • Formaat: PDF+DRM
  • Sari: Lecture Notes in Logic
  • Ilmumisaeg: 02-Mar-2017
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781316731543
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  • Formaat: PDF+DRM
  • Sari: Lecture Notes in Logic
  • Ilmumisaeg: 02-Mar-2017
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781316731543
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Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the tenth publication in the Lecture Notes in Logic series, Per Lindström presents some of the main topics and results in general metamathematics. In addition to standard results of Gödel et al. on incompleteness, (non-)finite axiomatizability, and interpretability, this book contains a thorough treatment of partial conservativity and degrees of interpretability. It comes complete with exercises, and will be useful as a textbook for graduate students with a background in logic, as well as a valuable resource for researchers.

Muu info

This volume presents some of the main areas and results of general metamathematics, including the results of Gödel et al. on incompleteness.
Chapter 0 Introduction
1(4)
Chapter 1 Preliminaries
5(18)
Exercises
20(2)
Notes
22(1)
Chapter 2 Incompleteness
23(19)
§1 Incompleteness
23(2)
§2 Consistency statements
25(6)
§3 Independent formulas
31(2)
§4 The length of proofs
33(2)
Exercises
35(5)
Notes
40(2)
Chapter 3 Numerations of r.e. sets
42(10)
§1 Numerations of r.e. sets
42(3)
§2 Types of independence
45(5)
Exercises
50(1)
Notes
51(1)
Chapter 4 Axiomatizations
52(10)
§1 Finite and bounded axiomatizability; reflection principles
52(5)
§2 Irredundant axiomatizability
57(2)
Exercises
59(2)
Notes
61(1)
Chapter 5 Partial conservativity
62(13)
Exercises
70(3)
Notes
73(2)
Chapter 6 Interpretability
75(19)
§1 Interpretability
75(9)
§2 Faithful interpretability
84(4)
Exercises
88(3)
Notes
91(3)
Chapter 7 Degrees of interpretabilty
94(25)
§1 Algebraic properties
94(8)
§2 A classification of degrees
102(2)
§3 Σ1 and Π1 degrees
104(10)
Exercises
114(3)
Notes
117(2)
Chapter 8 Generalizations
119(6)
§1 Incompleteness
119(2)
§2 Axiomatizations
121(1)
§3 Interpretability
122(2)
Notes
124(1)
References 125(5)
Index 130(2)
Notation 132
Per Lindström works in the Department of Philosophy at Göteborgs Universitet, Sweden.