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Elliott Mendelson — Introduction to mathematical logic
Elliott Mendelson — Introduction to mathematical logic



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Название: Introduction to mathematical logic

Автор: Elliott Mendelson

Аннотация:

The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in mathematical logic. This edition includes an extensive appendix on second-order logic, a section on set theory with urlements, and a section on the logic that results when we allow models with empty domains. The text contains numerous exercises and an appendix furnishes answers to many of them.Introduction to Mathematical Logic includes:opropositional logicofirst-order logicofirst-order number theory and the incompleteness and undecidability theorems of G?del, Rosser, Church, and Tarskioaxiomatic set theoryotheory of computabilityThe study of mathematical logic, axiomatic set theory, and computability theory provides an understanding of the fundamental assumptions and proof techniques that form basis of mathematics. Logic and computability theory have also become indispensable tools in theoretical computer science, including artificial intelligence. Introduction to Mathematical Logic covers these topics in a clear, reader-friendly style that will be valued by anyone working in computer science as well as lecturers and researchers in mathematics, philosophy, and related fields.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 1979

Количество страниц: 336

Добавлена в каталог: 08.12.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Partial function      7
Partial order      9 61 183
Partial recursive      227
Partial, permutation      263
Partial, potentially      263
Partial, relation      142
Partially Markov-computable      227
Particularization rule A4      73
Peano's postulates      121 122 134
Peter, R.      260
pf      169
Polish notation      19
Polyadic algebras      103
Possible definitions      171
Post, E.L.      239 256 264 265
Potentially recursive      263
Power class      179
Power of the continuum      8
Power set      181
Power set, axiom      181
PP      169
PR-formula      164
Precisely k-valid      72
Predecessor      260
Predicate, calculus      60
Predicate, letter      46
Predicate, pure monadic, calculus      170
Predicate, pure, calculus      90 169
Predicative wf      178
Premiss      30
Prenex normal form      88—92
Presburger, M.      134 266
Prime number      142 143
Prime power factorization      143
Primitive connectives      31
Primitive recursive function      138
Primitive recursive relation      142
Principal, connective      15
Principal, filter      108
Principal, letter      249
Principle of complete induction      8 9 131
Principle of dependent choice      214
Principle of Mathematical Induction      8 121 122
Principle, least-number      131
Principle, normalization      238
Principle, well-ordering      9 210
Product, cartesian      5 110 179
Production (simple, terminal)      222
Productive      264
Projection      228
Projection functions      135
proof      30 32
Proof, by contradiction      74
Proof, of an equation      249
Propagation      228
Proper axiom      59—60
Proper class      174
Proper ideal      10
Proper inclusion      173
Proper subset      5
Property      6 174
Proposition      31 32
Propositional calculus      12—44
Propositional calculus, intuitionistic      42
Propositional connective      11 13
PS      169
Pure first-order predicate calculus (PP)      90 169
Pure monadic predicate calculus      170
Putnam, H.      221 264
Quantifiers      45
Quantifiers, bounded      142
Quasi-quotation      31 (f.n.)
Quine, W.V.      4 13 219
Quotation marks      13 (f.n.)
Quotient (qt)      133 140
r.e.      see "Recursively enumerable"
Rabin, M.      167
Ramification      231
RANGE      6 180
Rank      214
Rasiowa, H.      67 (f.n.) 70 100 101
RE-formula      164
Recursion      138
Recursion, course-of-values      146
Recursive algorithm      236
Recursive function      138
Recursively (essentially) undecidable      166
Recursively axiomatizable      162
Recursively enumerable      260
Recursively equivalent      264
Reduced direct product      112
Reflexive      6
Reflexive partial order      9
Reflexive total order      9
Regular ordinal      205
Regularity, axiom of      213
Relation, arithmetical      151
Relation, binary      6 179
Relation, connected      183
Relation, equivalence      6
Relation, expressible      134
Relation, identity      6 180
Relation, irreflexive      183
Relation, membership      173 185
Relation, n-place      6
Relation, primitive recursive      142
Relation, recursive      142
Relation, reflexive      6
Relation, representing      137
Relation, symmetric      6
Relation, transitive      6 183
Relation, weakly expressible      262
Relative complement      5
Relatively interpretable      172
Relativization      172
Remainder (rm)      133 140
Replacement axiom      182
Replacement Theorem      75
Representable function      135
Representing relation      137
Rescher, N.      40
Restriction of a function      7 181
Richard's paradox      3
Rings, elementary theory of      82
Robinson's System      167
Robinson, A.      98 99 115 119
Robinson, J.      221
Robinson, R.M.      4 167 168 171 172 173 260
Rogers, H., Jr.      258 264 266
Rosenbloom, P.      103
Rosser, Goedel-, Theorem      160 162
Rosser, J.B.      4 40 41 78 88 160 217 219
RR      167
Rubin, J.      219
Rule A4      73
Rule C      76—78
Rule E4      73
Rules of Inference      30 249
Russell's paradox      2 4 183
Russell, B.      3 4
Ryll-Nardzewski, C.      167
S (first-order arithmetic)      121—122
S (first-order arithmetic), consistency of      126 163
S (first-order arithmetic), Goedel's Theorem for      159
Satisfaction relation      51—52 54
Satisfiable      56
Schema, algorithm      222
Schema, axiom      31
Scholz, H.      59 (f.n.) 172
Schroder-Bernstein Theorem      2 194
Schuette, K.      164
Scope      47
Second $\varepsilon$-Theorem      100
Section      185
Segment      185
Semantical      59 (f.n.) 70
Sentence      50
Sentence, atomic      15
Sequence (denumerable, finite)      8
Set      2 5 174
Set, Dedekind-finite      198
Set, denumerable      8 198
Set, empty (null)      5 175
Set, finite      197
Set, infinite      8 198
Set, power      181
Set, sum      180
Set, unit      5
Sets, disjoint      5
Sg, $\overline{sg}$      122
Shannon, C.      21
Shepherdson, J.      216 218
Shoenfield, J.      217 219
Sierpinski, W.      95 (f.n.) 208 209 217
Sikorski, R.      10 67 70 101 102
Similar ordered structures      184
Similar wfs      65
Similarity mapping      184
Simple production      222
Simple set      263
Simply transforms      223
Singular ordinal      218
Skolem normal form      90
Skolem — Loewenheim Theorem      71 84
Skolem — Loewenheim Theorem, Downward      108
Skolem — Loewenheim Theorem, Upward      107
Skolem — Loewenheim, Theorem      71 84
Skolem's paradox      196
Skolem, T.      219
Smullyan, R.      152 264
Sonner, J.      216
Specker, E.      217 219
Standard model      126
Standard part      117
State, internal      240 241
Statement form      13
Statement letter      13 31
Stone, M.      101
Strongly inaccessible ordinal      218
Strongly representable function      135
Stroyan, K.D.      119
Submodel      104
Subset      5
Subset, proper      5
Subsets, axiom of      181
Substitution      138
Substructure      104
Successor      121
Successor function      135
Successor ordinal      188
Sufficiently strong theory      172
Suitable      39
Sum class      179
Sum of cardinals      196
Sum set      180
Suppes, P.      219
Suranyi, J.      266
Symbol      29
symbols      240
symmetric      6
Syntactical      59 (f.n.) 70
System of equations      249
Szmielew, W.      98 267
Table, truth      11
Takeuti, G.      217
Tape      240
Tape, instantaneous, description      241
Tarski — Vaught theorem      106
Tarski's theorem      166
Tarski, A.      39 42 59 98 103 106 107 108 168 171 172 212 216 267
Tautology      16
Teichmueller — Tukey Lemma      211
Term      46 249
Term, closed      68
Terminal production      222
Terminally transforms      223
Theorem      30
Theory of equality      81
Theory, axiomatic      29
Theory, complete      66
Theory, first-order      59—60 61
Theory, formal      17 29
Theory, generalized first-order      95
Theory, recursively axiomatizable      162
Theory, recursively undecidable      166
Theory, sufficiently strong      172
Theory, type      4 219
Theory, with equality      79 83
Thompson, F.B.      103
Total function      7
Total order      9 183 184
Transfinite induction      9 187 189
Transitive class      185
Transitive closure      213
Transitive relation      6 183
Translation      239
Trichotomy      210
True wf      52
True, logically      17 57
Truth function      14 16
Truth table      11—15
Truth table, abbreviated      15
Truth values      11
Truth-functional combination      11
Turing algorithms      241
Turing machine      240—242
Turing, A.M.      239 240
Turing-computable      242
Turquette, A.R.      40
Tychonoff's theorem      99
Types, theory of      4 219
Ulam, S.      216
Ultra-filter      109
Ultrafilter      109
Ultrafilter, theorem      110
Ultrapower      112
Ultraproduct      112
Undecidable problems      265—266
Undecidable sentence      159
Undecidable theory      30
Undecidable, recursively      166
Uniformly continuous      119
union      5 177
Unit set      5
Universal algorithm      238
Universal choice function      212
UNIVERSAL class      177
Universal quantifiers      45
Univocal      181
Unordered pair      5 175
Unrestricted mu-operator      227
Upward Loewenheim — Skolem — Tarski Theorem      107
Upward Skolem — Loewenheim, Loewenheim — Tarski Theorem      107
Valid, logically      56
Van der Waerden, B.      98
Variable, free (bound)      48
Variable, individual      46
Vaughn, H.      100
Vaught, R.      96 106 108 216 218
von Neumann, J.      4 173 214
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