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Elliott Mendelson — Introduction to mathematical logic
 Обсудите книгу на научном форуме Нашли опечатку?Выделите ее мышкой и нажмите Ctrl+Enter 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: 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
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 -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,       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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