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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Negation theorem      131 163
Nice mapping      331
No Counterexample Interpretation      223
Nonlogical axiom      20 22
Nonlogical concept      9
Nonlogical symbol      14
Normal Form Theorem      157
Normalized      173
Novikoff's Theorem      324
Number variable      149
Numeral      126
Numerical instance      210
Occurrence      3
Occurrence Theorem      16
One-one reducible      191
Open formula      36
Open theory      48
Order      272
Ordered pair      243
Ordinal      246
Ordinal function symbol      272
PARAMETER      241
Part      69
Partial function      145
Partial functional      149
Partial mapping      144
Partial predicate      145
Partial relation      149
Partial subset      144
Peano arithmetic      204
Permutation      296
Positive formula      94
Positively calculable      121 149
Post’s theorem      167
Power set      242
Power set axiom      240
Predicate      10
Predicate symbol      14
Prefix      37
Prenex form      36 38
Prenex operations      37
Prime model      99
Primitive recursive      137
Principal type      90
Principle of Cofinality      239
Principle of complete induction      205
Principle of transfinite induction      247
Projection Lemma      168
Projective      175
proof      5
Proof by induction      5
Proof by transfinite induction      248
Propositional Axiom      21
Pure set      238
Quantifier      18
Quantifier Elimination Theorem      85
Quasi-tautology      49
R-formula      209
R-symbol      233
Rank      49 304
RE-index      158
RE-index from      167
Real closed field      87
Reative set      191
Recursion theorem      159
Recursive extension      206
Recursive function      109
Recursive in      164
Recursive ordinal      182
Recursive partial function      147
Recursive partial functional      150
Recursive partial predicate      147
Recursive partial relation      150
Recursive predicate      109
Recursive real number      137
Recursive relative to      164
Recursively enumerable degree      170
Recursively enumerable in      164 170
Recursively enumerable predicate      122
Recursively enumerable relation      150
Recursively inseparable      140
Recursively isomorphic      191
Recursively presented      324
Reduction      321
Reduction principle      201
Reduction Theorem      42
Reduction Theorem for Consistency      42
Regular cardinal      317
Regular model      230
Regular set of formulas      74
Regularity axiom      239
Relation      149 321
Replacement axiom      240
Replacement Lemma      165
Represent      126 127
Representability Theorem      128
Representable      127
Representing Function      108
Representing partial function      146
Representing partial functional      149
Restriction      43
Rosser’s Theorem      232
Rule (of inference)      4
Ryll-Nardjewski’s Theorem      91
Same kind      160 173
Same type      173
Sandwich      96
Satisfiable      67
Saturated      102
Scott’s Theorem      314
Second-Order Arithmetic      227

Semantical      3
separate      140 184
Separated      295
Separation principle      201
Separation theorem      184
Sequence number      116
Set      9 238
Set difference      243
Similar      252
Simple extension      47
Simple interpretation      135
Simply existential formula      83
Singular cardinal      317
Skolem form      67
Skolem’s Theorem      56
Special axiom      46
Special constant      46
Special equality axiom      52
Special sequence      49
Stage      238
Standard model      23 209 228
Strongly undecidable structure      134
Strongly undecidable theory      140
Structure      18
Submodel      73
Submodel condition      84
Subset axioms      239
Substitutible      17
Substitution rule      31
Substitution theorem      32
Substitution Theorem (in recursion theory)      155
Substructure      73
Successor      5 248
Surjective      71
Symbol      3
Symbol number      122
Symmetry Theorem      35
Syntactical      3
Syntactical variable      7
Tarski’s Lemma      77
Tautology      26
Tautology theorem      27
Teichmuller — Tukey lemma      47
Term      14
Theorem      1 4
Theorem on Consistency Proofs      213
Theorem on Constants      33
Theorem on Functional Extensions      55
Theory      22
Theory of a structure      82
Total function      145
Total functional      149
Total mapping      144
Total model      231
Total predicate      145
Total relation      149
Total subset      145
Totally recursive      195
Totally recursively enumerable      195
Transitive interpretation      262
Transitive set      246
Transitivity Lemma      164
Translation      58
TREE      180
Tree Theorem      180
TRUE      209 217 228
Truth definition      138
Truth function      11
Truth Lemma      286
Truth valuation      26
Truth value      11
Truth-table reducible      193
Tutological consequence      26
TYPE      89
Type recursive      223
Type symbol      215
Ultrafilter      104
Ultrapower      105
Ultraproduct      104
Unbounded $\mu$ -operator      112
Unbounded quantifier      113
Undecidable formula      45
Undecidable structure      139
Undecidable theory      123
Undefined expression      145
Uniformization theorem      188
Union of a chain      76
Union of sets      243
Union of theories      77
Uniqueness condition      59
Unit set      243
Universal formula      56
Universal quantifier      18
Universal structure      102
Universe      10 18 61
Unordered pair      243
Urelement      238
Valid      19 22 219
Validity Theorem      23
Variable      7 12 14 216
Variable-free      18
Variant      35
Variant Theorem      35
Weakly inaccessible      317
Weakly representable      139
Weakly saturated      102
Well-founded      198
Well-ordered      198 316
Well-ordering theorem      253
Word      321
Word problem      324
Zermelo — Fraenkel set theory      239

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