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Elliott Mendelson — Introduction to mathematical logic
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Название: Introduction to mathematical logicАвтор: 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 editionГод издания: 1979Количество страниц: 336Добавлена в каталог: 08.12.2013Операции: Положить на полку |
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"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 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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