Computability and Logic (3RD)

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Computability and Logic (3RD)

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  • 製本 Paperback:紙装版/ペーパーバック版
  • 言語 ENG
  • 商品コード 9780521389235
  • DDC分類 511.3

Table of Contents

Preface                                            ix (2)
Preface to the third edition xi
1 Enumerability 1 (10)
2 Diagonalization 11 (8)
3 Turing machines 19 (15)
4 Uncomputability via the busy beaver problem 34 (9)
5 Uncomputability via diagonalization 43 (9)
6 Abacus computable functions are Turing 52 (18)
computable
7 Recursive functions are abacus computable 70 (19)
8 Turing computable functions are recursive 89 (7)
9 First-order logic revisited 96 (16)
10 First-order logic is undecidable 112(9)
11 First-order logic formalized: 121(10)
derivations and soundness
12 Completeness of the formalization; 131(16)
compactness
13 The Skolem-Lowenheim theorem 147(10)
14 Representability in Q 157(13)
15 Undecidability, indefinability and 170(12)
incompleteness
16 Provability predicates and the 182(9)
unprovability of consistency
17 Non-standard models of arithmetic 191(6)
18 Second-order logic 197(10)
19 On defining arithmetical truth 207(5)
20 Definability in arithmetic and forcing 212(7)
21 The decidability of arithmetic with 219(9)
addition, but not multiplication
22 Dyadic logic is undecidable: 228(6)
`eliminating' names and function symbols
23 The Craig interpolation lemma 234(9)
24 Two applications of Craig's lemma 243(7)
25 Monadic versus dyadic logic 250(10)
26 Ramsey's theorem 260(8)
27 Provability considered modal-logically 268(17)
28 Undecidable sentences 285(8)
29 Non-standard models of Z are not recursive 293(8)
Index 301