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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
 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 in       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
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