Авторизация
Поиск по указателям
Elliott Mendelson — Introduction to mathematical logic
Обсудите книгу на научном форуме Нашли опечатку?
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 |
Скопировать ссылку для форума | Скопировать ID
Предметный указатель
First-order theory 59—60 First-order theory of densely ordered sets 81 First-order theory of equality 77 First-order theory, generalized 95 First-order theory, with equality 79 Fixed-point theorem 166 Form, statement 13 Formal theory 17 29 Formula, atomic 46 Formula, well-formed 29 46—47 Fraenkel, A.A. 219 Free for 48 Free occurrence 48 Free variable 48 Full iteration 232 Full normal forms 28 Fully equivalent algorithms 226 Function 7 181 Function, (strongly) representable 135 Function, characteristic 137 Function, definition of, letters 85 Function, initial 137 Function, letter 46 Function, partial 7 Function, primitive-recursive 138 Function, recursive 138 Function, total 7 Function, truth 14 16 Fundierungs-axiom 213 Fundierungsaxiom 213 Gabriel, P. 216 GCH see "Generalized continuum hypothesis" gen see "Generalization" General class existence theorem 178 General recursive see "Recursive" Generalization (Gen) 60 Generalized completeness theorem 101 Generalized Continuum Hypothesis 217 Generalized first-order theories 95 Gentzen, G. 164 Goedel number 151—152 235 Goedel's beta function 147 Goedel's completeness theorem 70 84 Goedel's second theorem 163—164 Goedel's Theorem for S 159 Goedel, K. 4 43 59 67 152 172 173 217 239 248 Graph 98 Grelling's paradox 3 Group theory 61 82 Group, orderable 99 Halmos, P. 10 100 103 Halpem, J.D. 103 Halting problem 266 Hartogs' theorem 200 Hasenjaeger, G. 59 67 172 Hatcher, W. 219 Hausdorff maximal principle 211 Heilman, M. 194 Henkin, L. 67 (f.n.) 95 98 103 Herbrand — Goedel computable 250 Herbrand — Goedel, computable 250 Herbrand, J. 32 70 239 248 Hermes, H. 239 248 Heterological 3 Heyting, A. 4 43 Higher-order theories 59 (f.n.) Higman, G. 265 Hilbert's tenth problem 221 Hilbert, D. 40 41 59 72 88 98 100 101 163 Hintikka, J. 67 (f.n.) 70 HYP 33 Hypothesis 30 33 Hypothesis, inductive 8 Ideal (maximal, proper) 10 Identity relation 6 180 Image 7 Immune 264 Implication, logical 16 56 Inaccessible ordinal 216 Inaccessible ordinal, weakly, strongly 218 included 5 inclusion 173 Inclusive "or" 12 Incompleteness, essential 163 Independence 38 Independent axiomatization 72 INDEX 236 255 263 Individual 160 Individual constants 46 Individual variables 46 Induction, complete 8 9 131 Induction, mathematical 8 121 122 Induction, rule 122 Induction, transfinite 9 187 189 Inductive hypothesis 8 Inference, rules of 30 249 Infinite 8 198 Infinitely close 117 Infinitesimal 116 117 Infinity, axiom of 182 Initial functions 137 Initial letter 249 Initial ordinal 200 Inner model 215 Instance 53 Instantaneous tape description 241 Internal states 240 241 Interpretable 171 Interpretable, relatively 172 Interpretations 50 Intersection 5 176 177 Intuitionism 4 Intuitionistic propositional calculus 42 Inverse 7 Inverse algorithm 210 Inverse image 7 Inverse of a word 224 Inverse relation 6 180 Iota term 88 Irreflexive 183 Isbell, J. 216 Isolated 264 Isomorphic 90 Isomorphic interpretations 93 Iteration 231 Iteration, full 232 Jaskowski, S. 43 Jech, T. 217 Jeroslow, R.G. 164 (f.n.) Joint denial 27 Juxtaposition 144 Juxtaposition, algorithm 229 k-valid 72 Kalmar, L. 37 171 Kamke, E. 94 95 Keisler, H.J. 98 119 Kelley, J. 219 Kleene, S.C. 40 42 43 59 88 152 168 195 239 248 251 254 255 265 Koenig's Unendlichkeitslemma 99 Krivine, J.L. 219 Kruse, A.H. 216 Kuratowski, K. 176 L 31 Lambda-computability 239 Langford, C.H. 97 Language (object and meta-) 32 (f.n.) Least element 9 Least number principle 131 Length of an expression 54 (f.n.) Letter, auxiliary 249 Letter, function 46 Letter, initial 249 Letter, predicate 46 Letter, principal 249 Letter, statement 13 31 Levy, A. 216 Lh (length) 143 Liar paradox 2 Limit ordinal 188 Limit point 119 Lindenbaum algebra 43 103 Lindenbaum's Lemma 66 93 Literal 28 Loewenheim, L., Downward Skolem-, -Tarski Theorem 108 Logic 1 Logic, many-valued 38—39 Logic, mathematical 1 4 Logical axioms 59—60 Logical consequence 16 56 Logical implication 16 56 Logically correct 24 Logically equivalent 16 56 Logically false 17 57 Logically true 17 57 Logically valid 56 Los's Theorem 113 Los, J. 93 99 113 Lukasiewicz, J. 42 Luxemburg, W.A.J. 119 MacLane, S. 216 Many-one reducible 263 Many-valued logic 38—39 Maps 7 Markov algorithm 223 Markov's Principle 238 Markov, A.A. 222 223 238 266 Markov-computable (partially) 227 Marriage problem 99—100 Mathematical induction 8 122 Matiyasevich, Yu. 221 265 Maximal element 199 Maximal ideal 10 Maximal ideal, theorem 101 Maximum 140 McKinsey, J.C.C. 39 Member 5 Membership relation 173 185 Mendelson, E. 10 116 121 122 214 Meredith, C.A. 42 Metalanguage 32 (f.n.) Metamathematics 32 (f.n.) Method of infinite descent 132 Minimal element 199 Minimum 140 Model 52 60 Model, contracted 83 Model, denumerable 67 Model, inner 215 Model, non-standard 126 134 Model, normal 83 Model, standard 126 modus ponens 31 Monadic predicate calculus, pure 170 Monadic predicate letter 46 Monk, J.D. 103 Montague, R. 216 218 Morley, M.D. 95 Morse — Kelley set theory 219 Morse, A. 219 Mostowski, A. 168 171 172 174 214 219 255 Moves 241 MP see "Modus ponens" Mu-operator 138 Mu-operator, bounded 142 Mu-operator, unrestricted 227 Multiplication, ordinal 190 Multiplicative axiom 9 210 Myhill, J. 263 264 Nagornyi, N. 240 Natural extension 228 Natural number 6 (f.n.) NBG 173 Negation 11 Negation rules 73 NF (Quine's New Foundations) 4 219 Nicod, J. 42 Non-class 174 Non-logical axioms 59—60 Non-logical constant 171 Non-standard analysis 116—119 Non-standard model 126 134 Non-standard natural numbers 117 Non-standard reals 116 Normal algorithm 223 Normal composition 228 Normal forms 28 Normal model 83 Normal prenex, forms 88—92 Normal Skolem, form 90 Normal system 239 Normalization principle 238 Novak-Gal, I.L. 219 Novikov, P.S. 265 Null set 5 175 Null set, axiom 175 Number, cardinal 2 8 196 215 Number, Goedel 151 235 Number, natural 6 (f.n.) Number, ordinal 185 Numeral 127 224 249 Object language 32 (f.n.) Occurrence (free, bound) 48 222 omega 188 Omega-consistency 158 Omega-incompleteness 160 One-one 7 181 One-one correspondence 7 One-one reducible 263 Onto function 7 Open set 119 Open wf 58 Operation 7 OR 12 Order, partial 9 61 183 Order, total 9 183 184 Order, well 9 183 Orderable group 99 Ordered k-tuple 5 176 Ordered pair 5 176 Ordinal of first kind 188 Ordinal, Addition 190 Ordinal, class 185 Ordinal, exponentiation 191 Ordinal, finite 188 197 Ordinal, inaccessible 216 218 Ordinal, initial 200 Ordinal, limit 188 Ordinal, Multiplication 190 Ordinal, number 185 Ordinal, regular, singular 218 Ordinal, successor 188 Owings, J.C., Jr. 13 Pair (unordered, ordered) 5 175 176 Pairing axiom 175 Paradox, logical 2 183 Paradox, semantic 2—5 Paradox, Skolem's 196 Parameters of a recursion 138 Parentheses 18—19 47 Partial 227
Реклама
in 
|
|
О проекте