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Monk J.D. — Mathematical Logic

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Название: Mathematical Logic

Автор: Monk J.D.

Аннотация:

From the Introduction: "We shall base our discussion on a set-theoretical foundation like that used in developing analysis, or algebra, or topology. We may consider our task as that of giving a mathematical analysis of the basic concepts of logic and mathematics themselves. Thus we treat mathematical and logical practice as given empirical data and attempt to develop a purely mathematical theory of logic abstracted from these data."

There are 31 chapters in 5 parts and approximately 320 exercises marked by difficulty and whether or not they are necessary for further work in the book.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1976

Количество страниц: 531

Добавлена в каталог: 29.11.2009

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Предметный указатель

$\alpha$ -sequence      408
$\mathscr{L}$ -closure conditions      395
$\mathscr{L}$ -structure      194
$\mathscr{L}_{fac}$ , $\mathscr{L}_{ind}$ -sequence      376
$\omega$ -complete      498
$\omega$ -completeness theorem      498
$\omega$ -consistent      247
$\Omega$ -logic      498
$\omega$ -structure      498
(m,n)-compact      500
(m,N)-relation      107
A priori      2
A-relation      31
Absolute      2
Absolutely free      387
abstract      2
Admissible function      313
Algebraic language      384
Algorithmic function      70
Algorithmic step      69
Applicability      3
Arithmetical hierarchy      85
Arithmetical relation      86
Arithmetization      12
ASSIGNMENT      495
atom      151
Atomic BA      151
Atomic equality formula      168
Atomic formula      168
Atomic nonequality formula      168
Atomless BA      151
Automorphism      352
Ax, J.      234
Axioms      208
Basic formula      233 235 238 240
Basic theorem on ultraproducts      322
Bell, J.      502
Beth's theorem      369
Beth, E.      6
Birkhoff, G.      391
Bishop, E.      5 7
Bolzano — Weierstrauss theorem      346
Boolean algebra      141
Boolean prime ideal theorem      150
Boolean representation theorem      150
Boone, W.      111
Bound occurrence      176
Cantor diagonal argument      47
Cantor, G.      350
Cardinality quantifier      500
Categorical theory      349
Chang, C.C.      217 310 400
Change of bound variable      181
Characteristic function      30
Characterization theorem      391
Characterizes      393
Chinese remainder theorem      57
Choice structure      481
Church's Theorem      293
Church's thesis      46
Church, A.      191 485
Closure      190
Cohen, P.      4 7
Collins, G.      296
Compact class      406
Compactness Theorem      6 204
complete      198
Complete computation      54
Complete configuration      53
Completeness theorem      6 122 123 204
Completeness theorem for equational logic      389
composition      27 77
Computation      16 69
Computation step      15
Computed by      50
Configuration      15
Congruence relation      385
Congruent modulo y      412
Conjunction symbol      162
Conjunctive normal form      128
Consequence      171
Conservative extension      208
Consistency family      311 312 473 506
Consistent      122 189
Consistent over      441
Construction sequence      116
Craig's interpolation theorem      365 506
Craig, W.      262
Creative set      97
Curry, H.      69 75
Cylindric algebra      219
Cylindric field of sets      219
Cylindric set algebra      219
Davis, M.      25 64 111
Decidable theory      233
Deduction Theorem      118 188
Defining relation      110
Definitional extension      208
Dekker, J.      111
Description operator      479
Descriptive triple      479
Detachment      117 171
Detlovs, V.      69 75
Diagram      329
Dickmann, M.      520
Diophantine equation      111
Discrete ordering      331
Disjunction symbol      162
Disjunctive normal form      127 235
Division algorithm      412
Downward Loewenheim — Skolem theorem      332
Duality principle      142
Dyson, V.      277
Effective definitional extension      208
Effective expansion      201
Effective function      12
Effective partial function      76
Effective procedure      11
Effective set      12
Effective Skolem expansion      211
Effectively calculable function      46
Effectively enumerable      12
Effectively enumerable set      92
Effectively incompletable      267
Effectively inseparable      100
Effectivized first-order language      164
Effectivized general logic      425
Ehrenfeucht, A.      234 406 412 417 419 444 450 453
Elementarily closed      406
Elementary class      393
Elementary diagram      337
Elementary effectivized first-order language      190
Elementary embedding      334
Elementary equivalent      327
Elementary extension      331
Elementary prime      445
Elementary recursive function      26
Elementary recursive operations      29
Elementary relation      30
Elementary substructure      331
Elimination of quantifiers      233
Embedding      320
Endomorphism      145
Engeler, E.      447
Equality symbol      162
equation      384
Erdoes, P.      517
Erfectivized relational version      206
Ershov, Yu.      234 242 260 264 277 280 296
Essentially undecidable      266

Exact      2
Existence condition      206
Existential formula      213 355
expansion      201 329
exponentiation      30
Expression      115 164
Extension      208 328
Factorial      30
Falsity      121
Feferman, S.      307 378
Field of sets      141
Fields of a tape      14
Filter      146 318
Filter generated by      148 427
Finite element      342
Finite extension      270
Finite intersection property      318
Finite presentation      110
Finitely inseparable      266
First occurrence      69
First-order language      162
Fixed point theorem      83 275
Formal proof      118 172
Formalism      4
Formula      168
Fraisse, R.      406 412 417 419
Frame      495
Free Boolean algebra      156
Free group      110
Free occurrence      176 177
Freely generated      156
Fuhrken, G.      501
Full language of a nonempty set      163 195
Functionally complete      129
General logic      418
General recursive function      45
General recursive operation      46
General recursive relation      46
General sentential logic      129
Generalization      171
Generalized product      377
Goedel numbering      12 52 53 54 77 121 154
Goedel — Herbrand — Kleene calculus      13 45 67
Goedel, K.      4 7 298
Gratzer, G.      392
Greatest lower bound      152
Grzegorczyk, A.      41
Gurevich, Yu.      234
Halmos, P.      160 228
Halpern, J.      296
Halting problem      82
Hanf number      337 340
Hanf system      336 340
Hanf, W.      277 509 511 517
Henkin's embedding theorem      330 339 340
Henkin, L.      228 311 329 442 502 520
Herbrand's theorem      213
Herbrand, J.      214
Hermes, H.      14 25 64 111
Heyting, A.      5 7
Hierarchy theorem      89
Hilbert $\epsilon$ -operator      481
Hilbert's tenth problem      111
Hilbert, D.      4 7 192
Holds in      196
Homogeneous structure      461
Homomorphism      145 223 385
Homomorphism theorem      147
Horn formula      398
Ideal      146 223
Ideal generated by      148 224
Identity      384
Implicational identity      398
Incompleteness      6
Independent      370
Independently axiomatizable      370
Indiscernibles      449
Individual constant      162
Individual variable      162
Induction on formulas      168
Induction on terms      167
Infinite digital computer      67
Infinite element      342
Infinitely close      345
Infinitesimal      344
Initial state      15
Inseparable      266
Intermediate Value Theorem      347
Interpretation      216
Intuitionism      4
Intuitionistic logic      137
Intuitionistic model      138
inversion      58
Isolated set      109
Isomorphic      145
Isomorphism      145 223 320 417
Iteration theorem      81
Janiczak, A.      234
Joint extension property      358
Jonsson, B.      392
Kalish, D.      485
Kalmar, L.      2 7
Keisler, H.J.      6 217 310 311 427 435 439 502 517 520
Kernel      147
Kleene, S.      90
Kochen, S.      234
Kreisel, G.      7
Laeuchli, H.      490 502
Lagrange, J.      282
Language of equality      163
Language of ordered fields      163
Language of rings      163
Language of set theory      163 195
Lavrov, I.      242 260 277 280 296
Law of excluded middle      5
Least upper bound      152
Lefschetz principle      351
Leisenring, A.      485
Liar paradox      276
Lies on      50
Lindenbaum, A.      200
Lindstrom, P.      6 417 424 425
Loeb, M.      299 307
Loewenheim — Skolem theorem      419 478
Loewenheim, L.      234
Logic without equality      473
Logical axiom      117 171
Logical theorem      171
Los — Vaught test      350
Los, J.      393 400
Lukasiewicz, J.      131 132
Lyndon, R.      403
m-atomic      444
m-atomless      444
m-basic model      353
m-categorical theory      349
m-consistent over n      428
m-elementary extension      352
m-elementary game      411
m-universal      461
Makkai, M.      311
Mal'cev, A.I.      90 102 234 279 280 485
Many-sorted language      483
Many-sorted logic      483
Markov algorithms      13 45 69
Markov, A.      75
Matiyasevic, Y.      111
Matrix      187
Maximal filter      149
Maximal ideal      149

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