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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
"Classical" sense      227 (f.n.)
$T_{k}$      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 $\mu$-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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