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Computability and Logic / Edition 5

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Overview

The third edition has been corrected and contains thoroughly revised versions of the chapters on Ramsey and probability, with new exercises provided for three other chapters. There are also two new chapters dealing with undecidable sentences.
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Editorial Reviews

From The Critics
This intermediate logic textbook for philosophy and computer science students introduces Gödel's completeness theorem, several incompleteness theorems, their attendant lemmas and corollaries, the theory of Turing machines, recursive functions, definability, and decidability. The fourth edition adds problems at the end of each chapter. Annotation c. Book News, Inc., Portland, OR (booknews.com)
From the Publisher
"John P. Burgess (Princeton U.) and Richard C. Jeffrey continue here in the tradition set by the late Boolos to present the "principal fundamental theoretical results </about/> logic" that would necessarily include the work of Gödel. For this edition they have revised and simplified their presentation of the representability of recursive functions, rewritten a section on Robinson arithmetic, and reworked exercises. They continue to present material in a two-semester format, the first on computability theory (enumerability, diagonalization, Turing compatibility, uncomputability, abacus computability, recursive functions, recursive sets and relations, equivalent definitions of computability) and basic metalogic (syntax, semantics, the undecidability of first-order logic, models and their existence, proofs and completeness, arithmetization, representability of recursive functions, indefinability, undecidability, incompleteness and the unprobability of inconsistency). They include a slate of nine further topics, including normal forms, second-order logic and Ramsey's theorem."
Book News, Inc.
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Product Details

  • ISBN-13: 9780521701464
  • Publisher: Cambridge University Press
  • Publication date: 9/30/2007
  • Edition description: Revised Edition
  • Edition number: 5
  • Pages: 366
  • Sales rank: 834,286
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.75 (d)

Table of Contents

Preface
1 Enumerability 3
2 Diagonalization 16
3 Turing Computability 23
4 Uncomputability 35
5 Abacus Computability 45
6 Recursive Functions 63
7 Recursive Sets and Relations 73
8 Equivalent Definitions of Computability 88
9 A Precis of First-Order Logic: Syntax 101
10 A Precis of First-Order Logic: Semantics 114
11 The Undecidability of First-Order Logic 126
12 Models 137
13 The Existence of Models 153
14 Proofs and Completeness 166
15 Arithmetization 187
16 Representability of Recursive Functions 199
17 Indefinability, Undecidability, Incompleteness 221
18 The Unprovability of Consistency 233
19 Normal Forms 243
20 The Craig Interpolation Theorem 260
21 Monadic and Dyadic Logic 270
22 Second-Order Logic 279
23 Arithmetical Definability 286
24 Decidability of Arithmetic without Multiplication 295
25 Nonstandard Models 302
26 Ramsey's Theorem 319
27 Modal Logic and Provability 327
Hints for Selected Problems 341
Annotated Bibliography 348
Index 349
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