Shoenfield J.R. — Mathematical Logic :: Электронная библиотека попечительского совета мехмата МГУ

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Shoenfield J.R. — Mathematical Logic

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Название: Mathematical Logic

Автор: Shoenfield J.R.

Аннотация:

Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. Topically, mathematical logic bears close connections to metamathematics, the foundations of mathematics, and theoretical computer science.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 352

Добавлена в каталог: 08.05.2014

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Предметный указатель

$\exists$ -Introduction Rule      21
$\forall$ -Introduction Rule      31
$\mu$ -operator      109
$\omega$ -model      231
Accessible set      305
Algebraically closed field      85
Alphabetical order      14
Amalgam      322
Amalgamation      322
Analytical Enumeration Theorem      175
Analytical hierarchy      174
Analytical Hierarchy Theorem      175
Analytical in      175
Analytical relation      173
Arithmetical Enumeration Theorem      163
Arithmetical hierarchy      160
Arithmetical Hierarchy Theorem      163
Arithmetical in      164
Arithmetical relation      160
Associate      331
Association to the right      17
Associative Rule      21
Atomic formula      15 217
Automorphism      97
Axiom      1 4
Axiom of Choice      253
Axiom of constructibility      277
Axiom of infinity      240
Axiom of Measurability      307
Axiomatizable      138
Axiomatized      125
Banach — Ulam Theorem      308
Basic concept      1
Basis      185
Belong      48
Benign      327 329
Bijective      71
Borel relation      179
Bound      13 16
Bounded $\mu$ -operator      112
Bounded quantifier      113
Boundedness Theorem      184
Calculable      107 144 145 149
Canonical structure      44
Cantor’s theorem      258
Cardinal      254
Cardinal of a model      78
Cardinality Theorem      78
Cartesian product      244
Categorical      88
Chain      76
Chang — Los — Suszko Theorem      77
Characterization Problem      41
Characterization theorem      185
Choice function      253
Church’s Theorem      131
Church’s thesis      119
class      9 238
Classical axiom system      2
Closed formula      19
Closed set      257
Closure Theorem (for formulas)      32
Closure Theorem (for sets)      257
Compactness Theorem      69
Compatible designators      15
Compatible theories      140
Complete predicate      193
Complete predicate symbol      266
Complete theory      45 82
Completely recursive      194
Completely recursively enumerable      194
Completeness theorem      43
Comprehension axiom      228
Conclusion      4
Condition      282
Conjunction      18
Conjunctive form      40
Consequence      20 322
Conservative extension      41
Consistency theorem      49
Consistent      42
Constant      14 216
Constructible set      272
Continuum Hypothesis      259
Contraction      117 165
Contraction formulas      118
Contraction of quantifiers      152
Contraction rule      21
Countable language      78
Countable set      255
Countable theory      78
Cut rule      21
Decidable formula      45
Decidable theory      123
Decision method      106 107 144 145 148 149
Decision problem      106 107
Deduction Theorem      33
Definability Theorem      81
Definable      80 81 135
Defined formula      6
Defined symbol      6
Defining axiom      57 59
Defining equation      216
Defining relation      322
Definition      6
Definition by cases      113
Definition by transfinite induction      250
Degree      169
Derived concept      1
Descending sequence      180
Designator      15
Detachment rule      28
Diagonal Lemma      130
Diagram      74
Diagram Lemma      74
Direct product      94
Disjoint      184
Disjunction      18
Disjunctive form      40
Distribution rule      32
Domain      144
Effectively recursively inseparable      192
Ehrenfeucht’s Theorem      90
Elementarily equivalent      72
Elementarily prime model      104
Elementary chain      77
Elementary class      92
Elementary extension      74
Elementary formula      26
Elementary substructure      74
Elementary theory of algebraically closed fields      85
Elementary theory of fields      70
Elementary theory of groups      22
Elementary theory of ordered fields      87
Elimination of quantifiers      83
Embedding      72
Enumerates      138 158
Enumeration theorem      158
Equality axiom      21
Equality predicate      10
Equality symbol      14
Equality theorem      42
EQUIVALENCE      18
Equivalence theorem      34
Equivalent formulas      83
Equivalent functions or predicates      169
Equivalent theories      42
Essentially undecidable theory      140
Existence condition      59 206 242 245
Existential formula      52

Existential quantifier      18
expansion      43
Expansion by definitions      134
Expansion Rule      21
Explicit definition      110
Expression      3
Expression number      122
Extension (of a condition)      282
Extension (of a language or theory)      41
Extension (of a sequence number)      179
Extension (of a structure)      73
Extension by definitions      60
Extensionality axiom      228
Faithful interpretation      184
Finitary proof      3 51
Finite character      47
Finite extension      134
Finite ordinal      249
Finite rule      5
Finite set      255
Finitely axiomatized      69
Finitely generated      93
Finitely presented      323
Finiteness lemma      165
First ordinal      247
First-order language      14 15
First-order theory      22
Forcing      283 297
Formal system      3
Formation Theorem      16
Formula      3 15 217
free      13 16 321
Free group      321
Free product      322
Friedberg — Muchnik Theorem      170
Function      10 245
Function symbol      14
Function variable      149
Functional      149
Functional index      168
Functional of type r      215
Functional RE-index      168
Functionally arithmetical      168
Functionally enumerates      168
Functionally recursive      168
Functionally recursively enumerable      168
Generalization      18
Generalization rule      31
Generalized axiom of infinity      304
Generalized Continuum Hypothesis      259
Generalized elementary class      92
Generalized formula      218
Generalized inductive definition      4
Generator      90 322
GENERIC      283
Graph      146 150
H-index      176
H-index from      179
Hanf — Tarski Theorem      313
Height      15
Henkin theory      45
Henkin — Orey Theorem      231
Herbrand’s theorem      54
Hereditarily undecidable      141
Higman group      325
Higman’s theorem      325
Homogeneous structure      102
Homomorphic image      94
Homomorphism      94
Horn formula      95
Hyperarithmetical function      185
Hyperarithmetical in      179
Hyperarithmetical relation      176
Hyperdegree      199
Hyperjump      199
Hypothesis      4
Identity axiom      21
Implication      18
Implicit definition      159 188
Inaccessible      304
Incompleteness theorem      132
Inconsistent      42
INDEX      157
Index from      167
Individual      10 18
Individual function      10
Individual predicate      10
Individual variable      12
Induction axiom      204 228
Induction hypothesis      5
Induction on predicate symbols      261
Induction on recursive functions      109
Induction on theorems      5 31
Induction rule      229
Inessential expansion      141
Infinite element      234
Infinite ordinal      249
Infinite set      255
Infinity lemma      187
Injective      71
Instance      19 31
Instantiation      18
Interpretable      64
Interpretation      61 62
Interpretation Theorem      62
Intersection      243
Introduce      205 218
Invariant      263 297 326 332
Isomorphic      71
Isomorphism (of interpretations)      260
Isomorphism (of structures)      71 81
Isomorphism condition      84
Joint Consistency Theorem      79
Kleene basis theorem      186
Kreisel Basis Theorem      187
Language      3
Least number principle      205
Level      46
Limit ordinal      241
Lindenbaum’s Theorem      47
Loewenheim — Skolem theorem      79
Logical axiom      20 21
Logical concept      9
Logical consequence      20
Logical symbol      14
Logically valid      20
Los — Tarski Theorem      76
Los — Vaught Theorem      89
m-language      78
M-theory      78
Many-one reducible      191
Mapping      9
Masure ideal      307
Matrix      37
Maximal element      47
McKinsey formula      95
Measurable      307
Minimal element      239
Minimal ordinal      247
Model      22
Model Extension Theorem      75
Model-complete      99
Modern axiom system      2
Morphism      93
Multiplicative axiom      292
n-ary      10 14
n-equivalent      101
NAME      18
Natural number      4 249
Negation      18

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