Электронная библиотека Попечительского советамеханико-математического факультета Московского государственного университета
 Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум Авторизация Поиск по указателям     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
 "Classical" sense      227 (f.n.) 165 Abbreviated truth table      15 abbreviations      31 (f.n.) Abelian group      82 Absolute consistency      37 AC      see "Axiom of Choice" Ackermann, W.      40 41 260 266 Addition, ordinal      190 Adequate sets of connectives      25—28 Algebra, boolean      43 Algebra, cylindrical      103 Algebra, Lindenbaum      43 103 Algebra, polyadic      103 Algorithm      222 Algorithm, (fully) equivalent      226 Algorithm, closed      227 Algorithm, doubling      225 240 Algorithm, iteration      231 Algorithm, juxtaposition      229 Algorithm, Markov      223 Algorithm, normal      223 Algorithm, projection      228 Algorithm, ramification      218 Algorithm, recursive      236 Algorithm, schema      222 Algorithm, Turing-computable      242 Algorithm, universal      238 Alphabet      222 Alphabet of a Turing machine      240 241 Alternative denial      27 AND      11 Antecedent      12 applicable      222 Arguments, of a function      7 Arguments, of a relation      6 Arithmetical relation      151 Arithmetization      152 Atomic formula      46 Atomic sentence      15 Autological      3 Autonomous symbols      31 (f.n.) Auxiliary letter      249 Axiom      29 Axiom of Choice      9 210 Axiom of extensionality      175 Axiom of infinity      182 Axiom of null set      175 Axiom of regularity      213 Axiom of subsets      181 Axiom, finite, of choice      211 Axiom, logical      59—60 Axiom, multiplicative      9 210 Axiom, Pairing      175 Axiom, power set      181 Axiom, proper (non-logical)      59—60 Axiom, Replacement      182 Axiom, schemas      31 Axiomatic set theory      4 173 Axiomatic theory      29 Axiomatizable, finitely      167 Axiomatizable, recursively      162 Axiomatization, independent      72 Axiomatizations of the propositional calculus      40 Axioms of class existence      176 Bachmann, H.      209 Bar-Hillel, Y.      219 Bernays, P.      4 59 72 88 98 100 101 163 173 216 263 Bernstein, A.R.      119 Bernstein, F.      see "Schroeder — Bernstein Theorem" Berry's paradox      3 Beta function of Goedel      147 Beth, E.W.      67 70 98 168 Biconditional      13 Biconditional rules      74 Binary predicate letter      46 Binary relation      6 Bolzano — Weierstrass theorem      119 Boolean algebra      9 43 Boolean representation theorem      100 Boone, W.      265 Bound occurrence      48 Bound variable      48 Bound variable, change of      75 Bounded -operator      142 Bounded quantifiers      142 Bounded sums and products      141 Bourbaki, N.      94 Britton, J.      265 Brouwer, L.E.J.      4 Burali-Forti's paradox      2 4 183 Cantor's paradox      2 4 183 Cantor's theorem      2 195 cardinal number      2 8 196 215 Carnap, R.      31 (f.n.) Cartesian product      5 110 179 Categorical      93 134 Causal laws      12 (f.n.) Chain      210 Chang, C.C.      98 Change of bound variables      75 Characteristic function      137 Characteristic of a field      98 Cherlin, G.      98 Chinese remainder theorem      151 Choice, axiom of      9 210 Choice, denumerable axiom of      214 Choice, finite axiom of      211 Choice, function      210 Choice, principle of dependent      214 Choice, set      9 210 Choice, universal, function      212 Chuquai, R.      219 Church's Theorem      170 Church's thesis      163 238 239 Church, A.      42 59 171 219 239 Circuit, electric      21 class      5 (f.n.) 174 Class, existence axioms      176 Class, general, existence theorem      178 Closed normal algorithm      227 Closed set      119 Closed term      68 Closed wf      50 Closure      53 Closure, transitive      213 Cohen, P.J.      217 Compactness      71 115 Compatible theories      168 Complement      176 177 Complement, relative      5 Complete diagram      107 Complete induction      8 9 131 Complete theory      66 Completeness theorem, for L      37 Completeness theorem, generalized      101 Completeness theorem, Goedel's      70 Component      110 composition      7 193 Composition (normal) of algorithms      228 Computable      221 Computable, (partially) Markov-      227 Computable, Herbrand — Goedel      250 Computation of a Turing machine      242 Conditional      12 Conjunct      11 Conjunction      11 conjunction rule      73 Conjunctive normal form      28 Connected relation      183 Connective      11 13 39 Connective, primitive      31 Connective, principal      15 Consequence      30 Consequence, logical      16 56 Consequent      12 Consistency of L      37 Consistency of predicate calculus      62 85 Consistency of S      126 163 Consistency, absolute      37 Consistency, omega-consistency      158 Constant, individual      46 Constant, non-logical      171 continuous      118 Continuous, uniformly      119 Continuum      8 Continuum Hypothesis      217 Contracted model      83 Contradiction      17 Contradiction, proof by      74 Contradictory      56 Contrapositive      21 Correspondence, one-one      7 Countable      8 Counter-factual      13 (f.n.) Counter-factual conditional      13 (f.n.) Course-of-values recursion      146 Craig, W.      262 Creative      263 Cretan "paradox"      2 (f.n.) Cylindrical algebra      103 Davis, M.      119 221 243 266 de Bruijn, N.      99 Decidable      30 Decidable, effectively      162 Decision problem      265 Dedekind, R.      103 121 Dedekind-finite      198 Dedekind-infinite      199 Deduction      30 Deduction, theorem for first-order theories      62—63 Deduction, theorem for L      32 Definite description      88 Definition, by cases      144 Definition, by transfinite induction      189 Dekker, J.      264 Densely-ordered sets, theory of      81 Denumerable      8 198 Denumerable axiom of choice      214 Denumerable model      67 Denumerable sequence      8 Dependent choice, principle of      214 Depends      62 Derivable      249 Derived rules      73—74 Designated values      39 Diagram (complete)      107 Difference      177 Direct consequence      30 Direct product      113 Direct product, reduced      112 Dirichlet's theorem      134 Disjoint sets      5 Disjunct      12 Disjunction      12 Disjunction, rules      74 Disjunctive normal form      28 Divisibility      132 Domain      6 176 177 Domain of an interpretation      50 Doubling algorithm      225 240 Downward Loewenheim — Skolem — Tarski Theorem      108 Drake, F.      219 Dreben, B.      70 Dual      75 Duality      21 76 Dummy variables      139 Dyson, V.H.      151 Easton, W.B.      212 Effective      30 59 221 Effectively computable      221 Effectively decidable      30 162 Ehrenfeucht, A.      134 264 Electric circuit      21 Element      5 Elementarily equivalent      103 Elementary, extension      105 Elementary, submodel      105 Elementary, substructure      105 Elementary, theory      82 Elimination of existential quantifiers      97—98 Empty set      5 Empty word      222 Epimenides      2 (f.n.) EPSILON      5 173 Epsilon, relation      176 Epsilon, second, theorem      100 Equality      5 Equality in set theory      173 Equality, theories with      79 83 Equality, theory of      81 equation      249 Equinumerous      2 7 192 Equivalence theorem      74 Equivalence, class      6 Equivalence, logical      16 56 Equivalence, recursive      264 Equivalent algorithms      226 Equivalent, elementarily      103 Erdoes, P.      99 216 Essential incompleteness      163 Essential undecidability      151 Essentially recursively undecidable      151 Exceptional statement form      39 Exclusive "or"      12 Existential quantifier      45 47 227 Existential rule E4      73 Exponentiation, ordinal      191 Expressible relation      134 Expressible relation, weakly      262 Expression      29 Extension of a model      104 Extension of a theory      66 Extension of an alphabet      222 Extension, finite      168 Extension, natural      228 Extensionality axiom      175 Extremal clause      31 (f.n.) False wf      52 False, logically      17 57 Falsity (F)      12 Feferman, S.      163—164 264 Feigner, U.      212 217 Fermat's last theorem      145 Fibonacci sequence      147 Field of a relation      6 184 Field, algebraically closed      99 Field, elementary theory of      82 98 Field, real-closed      267 Filter      108 Filter, proper, improper, principal      108 Finitary      32 (f.n.) Finite axiom of choice      211 Finite character      211 Finite extension      168 Finite ordinal      188 197 Finite sequence      8 Finite set      8 197 Finitely axiomatizable      167 First-order predicate calculus      60
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