Computability and Logic by George S. Boolos, John P. Burgess, Richard C. Jeffrey | | Hardcover | Barnes & Noble
Computability and Logic / Edition 5

Computability and Logic / Edition 5

5.0 1
by George S. Boolos, John P. Burgess, Richard C. Jeffrey
     
 

ISBN-10: 0521877520

ISBN-13: 9780521877527

Pub. Date: 09/30/2007

Publisher: Cambridge University Press

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.

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.

Product Details

ISBN-13:
9780521877527
Publisher:
Cambridge University Press
Publication date:
09/30/2007
Edition description:
Revised
Pages:
364
Product dimensions:
6.14(w) x 9.21(h) x 0.83(d)

Table of Contents

Preface to the Fifth Edition     xi
Computability Theory
Enumerability     3
Enumerability     3
Enumerable Sets     7
Diagonalization     16
Turing Computability     23
Uncomputability     35
The Halting Problem     35
The Productivity Function     40
Abacus Computability     45
Abacus Machines     45
Simulating Abacus Machines by Turing Machines     51
The Scope of Abacus Computability     57
Recursive Functions     63
Primitive Recursive Functions     63
Minimization     70
Recursive Sets and Relations     73
Recursive Relations     73
Semirecursive Relations     80
Further Examples     83
Equivalent Definitions of Computability     88
Coding Turing Computations     88
Universal Turing Machines     94
Recursively Enumerable Sets     96
Basic Metalogic
A Precis of First-Order Logic: Syntax     101
First-Order Logic     101
Syntax     106
A Precis of First-Order Logic: Semantics     114
Semantics     114
Metalogical Notions     119
The Undecidability of First-Order Logic     126
Logic and Turing Machines     126
Logic and Primitive Recursive Functions     132
Models     137
The Size and Number of Models     137
Equivalence Relations     142
The Lowenheim-Skolem and Compactness Theorems     146
The Existence of Models     153
Outline of the Proof     153
The First Stage of the Proof     156
The Second Stage of the Proof     157
The Third Stage of the Proof     160
Nonenumerable Languages     162
Proofs and Completeness     166
Sequent Calculus     166
Soundness and Completeness     174
Other Proof Procedures and Hilbert's Thesis     179
Arithmetization     187
Arithmetization of Syntax     187
Godel Numbers     192
More Godel Numbers     196
Representability of Recursive Functions     199
Arithmetical Definability     199
Minimal Arithmetic and Representability     207
Mathematical Induction     212
Robinson Arithmetic      216
Indefinability, Undecidability, Incompleteness     220
The Diagonal Lemma and the Limitative Theorems     220
Undecidable Sentences     224
Undecidable Sentences without the Diagonal Lemma     226
The Unprovability of Consistency     232
Further Topics
Normal Forms     243
Disjunctive and Prenex Normal Forms     243
Skolem Normal Form     247
Herbrand's Theorem     253
Eliminating Function Symbols and Identity     255
The Craig Interpolation Theorem     260
Craig's Theorem and Its Proof     260
Robinson's Joint Consistency Theorem     264
Beth's Definability Theorem     265
Monadic and Dyadic Logic     270
Solvable and Unsolvable Decision Problems     270
Monadic Logic     273
Dyadic Logic     275
Second-Order Logic     279
Arithmetical Definability     286
Arithmetical Definability and Truth     286
Arithmetical Definability and Forcing     289
Decidability of Arithmetic without Multiplication     295
Nonstandard Models     302
Order in Nonstandard Models     302
Operations in Nonstandard Models      306
Nonstandard Models of Analysis     312
Ramsey's Theorem     319
Ramsey's Theorem: Finitary and Infinitary     319
Konig's Lemma     322
Modal Logic and Provability     327
Modal Logic     327
The Logic of Provability     334
The Fixed Point and Normal Form Theorems     337
Annotated Bibliography     341
Index     343

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