Computability and Logic

Recommendations

Info

278 MONADIC AND DYADIC LOGIC Svu is not to hold in any other cases. Note that (2) (3) if Svu, then v + 1 ≥ u there is at most one u
Page 2:
This page intentionally left blank
Page 8:
Computability and Logic Fifth Editi
Page 12:
For SALLY and AIGLI and EDITH
Page 18:
viii CONTENTS BASIC METALOGIC 9 APr
Page 24:
Preface to the Fifth Edition The or
Page 28:
PREFACE TO THE FIFTH EDITION xiii T
Page 36:
1 Enumerability Our ultimate goal w
Page 40:
1.1. ENUMERABILITY 5 we might have
Page 44:
1.2. ENUMERABLE SETS 7 member of A,
Page 48:
1.2. ENUMERABLE SETS 9 The pair (m,
Page 52:
1.2. ENUMERABLE SETS 11 a pair G(n)
Page 56:
1.2. ENUMERABLE SETS 13 on Example
Page 60:
PROBLEMS 15 the set of all positive
Page 64:
DIAGONALIZATION 17 supposition must
Page 68:
DIAGONALIZATION 19 has that much ti
Page 72:
PROBLEMS 21 2.4 Show that the set o
Page 76:
3 Turing Computability A function i
Page 80:
TURING COMPUTABILITY 25 carried out
Page 84:
TURING COMPUTABILITY 27 in general
Page 88:
TURING COMPUTABILITY 29 It will the
Page 92:
TURING COMPUTABILITY 31 But if ther
Page 96:
TURING COMPUTABILITY 33 A numerical
Page 100:
4 Uncomputability In the preceding
Page 104:
4.1. THE HALTING PROBLEM 37 machine
Page 108:
4.1. THE HALTING PROBLEM 39 Turing
Page 112:
4.2. THE PRODUCTIVITY FUNCTION 41 g
Page 116:
4.2. THE PRODUCTIVITY FUNCTION 43 F
Page 120:
5 Abacus Computability Showing that
Page 124:
5.1. ABACUS MACHINES 47 be thought
Page 128:
5.1. ABACUS MACHINES 49 Figure 5-4.
Page 132:
5.2. SIMULATING ABACUS MACHINES BY
Page 136:
Page 140:
Page 144:
5.3. THE SCOPE OF ABACUS COMPUTABIL
Page 148:
5.3. THE SCOPE OF ABACUS COMPUTABIL
Page 152:
PROBLEMS 61 Figure 5-17. Minimizati
Page 156:
6 Recursive Functions The intuitive
Page 160:
One might indicate this in shorthan
Page 164:
6.1. PRIMITIVE RECURSIVE FUNCTIONS
Page 168:
6.1. PRIMITIVE RECURSIVE FUNCTIONS
Page 172:
PROBLEMS 71 The total function f is
Page 176:
7 Recursive Sets and Relations In t
Page 180:
7.1. RECURSIVE RELATIONS 75 Given a
Page 184:
7.1. RECURSIVE RELATIONS 77 Proof:
Page 188:
7.1. RECURSIVE RELATIONS 79 So the
Page 192:
answer. Thus if S is a semidecidabl
Page 196:
7.3. FURTHER EXAMPLES 83 Proof: Sup
Page 200:
7.3. FURTHER EXAMPLES 85 after whic
Page 204:
PROBLEMS 87 7.9 Let f (n) bethenth
Page 208:
8.1. CODING TURING COMPUTATIONS 89
Page 212:
Page 216:
Page 220:
8.2. UNIVERSAL TURING MACHINES 95 P
Page 224:
PROBLEMS 97 relation of the restric
Page 228:
Basic Metalogic
Page 234:
102 APRÉCIS OF FIRST-ORDER LOGIC:
Page 238:
Page 242:
Page 246:
Page 250:
Page 254:
Page 258:
10 APrécis of First-Order Logic: S
Page 262:
Page 266:
Page 270:
Page 274:
Page 278:
Page 282:
11 The Undecidability of First-Orde
Page 286:
128 THE UNDECIDABILITY OF FIRST-ORD
Page 290:
Page 294:
Page 298:
Page 302:
Page 306:
138 MODELS There are actually sever
Page 310:
140 MODELS If we also let 0 denote
Page 314:
142 MODELS But this is simply the c
Page 318:
144 MODELS the number of equivalenc
Page 322:
146 MODELS elements are isolated, a
Page 326:
148 MODELS (b) Any set of sentences
Page 330:
150 MODELS vertices of a square, an
Page 334:
152 MODELS Such a model A will cons
Page 338:
154 THE EXISTENCE OF MODELS (S7) If
Page 342:
156 THE EXISTENCE OF MODELS 13.6 Le
Page 346:
158 THE EXISTENCE OF MODELS (E3) If
Page 350:
160 THE EXISTENCE OF MODELS which i
Page 354:
162 THE EXISTENCE OF MODELS And ind
Page 358:
164 THE EXISTENCE OF MODELS Problem
Page 362:
14 Proofs and Completeness Introduc
Page 366:
168 PROOFS AND COMPLETENESS true.
Page 370:
170 PROOFS AND COMPLETENESS Table 1
Page 374:
172 PROOFS AND COMPLETENESS is beca
Page 378:
174 PROOFS AND COMPLETENESS 14.13 E
Page 382:
176 PROOFS AND COMPLETENESS new int
Page 386:
178 PROOFS AND COMPLETENESS whether
Page 390:
180 PROOFS AND COMPLETENESS possibl
Page 394:
182 PROOFS AND COMPLETENESS Proofs:
Page 398:
184 PROOFS AND COMPLETENESS In addi
Page 402:
186 PROOFS AND COMPLETENESS Unless
Page 406:
188 ARITHMETIZATION in which, as el
Page 410:
190 ARITHMETIZATION 15.5 Corollary
Page 414:
192 ARITHMETIZATION 15.7 Corollary.
Page 418:
194 ARITHMETIZATION This means that
Page 422:
196 ARITHMETIZATION For the first c
Page 426:
198 ARITHMETIZATION 15.2 Let Ɣ be
Page 430:
200 REPRESENTABILITY OF RECURSIVE F
Page 434:
Page 438:
Page 442:
Page 446:
Page 450:
Page 454:
Page 458:
Page 462:
Page 466:
Page 470:
17 Indefinability, Undecidability,
Page 474:
222 INDEFINABILITY, UNDECIDABILITY,
Page 478:
Page 482:
Page 486:
Page 490:
Page 494:
18 The Unprovability of Consistency
Page 498:
234 THE UNPROVABILITY OF CONSISTENC
Page 502:
Page 506:
Page 512:
Further Topics
Page 518:
244 NORMAL FORMS Proof: The proof i
Page 522:
246 NORMAL FORMS 19.3 Theorem (Full
Page 526:
248 NORMAL FORMS For (1) and (3.1)
Page 530:
250 NORMAL FORMS can be the domains
Page 534: 252 NORMAL FORMS as ‘set (of natu
Page 538: 254 NORMAL FORMS Now if Ɣ is satis
Page 542: 256 NORMAL FORMS in a sense to be m
Page 546: 258 NORMAL FORMS if P A holds of a
Page 550: 20 The Craig Interpolation Theorem
Page 554: 262 THE CRAIG INTERPOLATION THEOREM
Page 570: 21 Monadic and Dyadic Logic We have
Page 574: 272 MONADIC AND DYADIC LOGIC associ
Page 578: 274 MONADIC AND DYADIC LOGIC Our in
Page 582: 276 MONADIC AND DYADIC LOGIC For th
Page 588: 22 Second-Order Logic Suppose that,
Page 592: SECOND-ORDER LOGIC 281 (The foregoi
Page 596: SECOND-ORDER LOGIC 283 22.6 Example
Page 600: PROBLEMS 285 Problems 22.1 Does it
Page 604: 23.1. ARITHMETICAL DEFINABILITY AND
Page 620: 24 Decidability of Arithmetic witho
Page 624: DECIDABILITY OF ARITHMETIC WITHOUT
Page 628: DECIDABILITY OF ARITHMETIC WITHOUT
Page 632: PROBLEMS 301 if there are rational
Page 636:
25.1. ORDER IN NONSTANDARD MODELS 3
Page 640:
25.1. ORDER IN NONSTANDARD MODELS 3
Page 644:
25.2. OPERATIONS IN NONSTANDARD MOD
Page 648:
Page 652:
Page 656:
25.3. NONSTANDARD MODELS OF ANALYSI
Page 660:
25.3. NONSTANDARD MODELS OF ANALYSI
Page 664:
PROBLEMS 317 (In general, there cou
Page 668:
26 Ramsey’s Theorem Ramsey’s th
Page 672:
26.1. RAMSEY’S THEOREM: FINITARY
Page 676:
26.2. K ÖNIG’S LEMMA 323 called
Page 680:
26.2. K ÖNIG’S LEMMA 325 The pre
Page 684:
27 Modal Logic and Provability Moda
Page 688:
27.1. MODAL LOGIC 329 There is a no
Page 692:
27.1. MODAL LOGIC 331 deducible fro
Page 696:
27.1. MODAL LOGIC 333 For Propositi
Page 700:
27.2. THE LOGIC OF PROVABILITY 335
Page 704:
27.3. THE FIXED POINT AND NORMAL FO
Page 708:
27.3. THE FIXED POINT AND NORMAL FO
Page 712:
Annotated Bibliography General Refe
Page 718:
344 INDEX categorical theory, see d
Page 722:
346 INDEX Gödel sentence, 225 Göd
Page 726:
348 INDEX Presburger, Max, see arit
Page 730:
350 INDEX valid sentence, 120, 327
show all

Computability and Logic

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?