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Elliott Mendelson — Introduction to mathematical logic
Elliott Mendelson — Introduction to mathematical logic



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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: en

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
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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 $+x_{i}$ in $\mathfrak{A}$      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
1 2 3 4
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