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Hirschfeld J., Wheeler W.H. Ч Forcing, Arithmetic, Division Rings
Hirschfeld J., Wheeler W.H. Ч Forcing, Arithmetic, Division Rings

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Ќазвание: Forcing, Arithmetic, Division Rings

јвторы: Hirschfeld J., Wheeler W.H.

язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1975

 оличество страниц: 266

ƒобавлена в каталог: 15.08.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$a_{\Simga}$, $s_T$      31 see
$S_E$      160
$T^f$      89 see finite also
$\forall_n$-extension of a structure      104Ч107
$\mathcal{E}_{\Sigma}, \mathcal{E}_T$      16Ч17 see
$\mathcal{F}_T$      96 see finitely also
$\mathcal{G}_{\Sigma}, \mathcal{G}_T$      57 see infinitely also
$\mathcal{L}_{k, \omega}$-equivalence, $\mathcal{L}_{k, \omega}$-substructure, $\mathcal{L}_{k, \omega}$-equivalence, $\mathcal{L}_{\infty, \omega}$-substructure      9
$\mathcal{L}_{k, \omega}$-equivalence, $\mathcal{L}_{k, \omega}$-substructure, $\mathcal{L}_{k, \omega}$-equivalence, $\mathcal{L}_{\infty, \omega}$-substructure, for existentially complete division algebras      215Ч216
$\mathcal{L}_{k, \omega}$-equivalence, $\mathcal{L}_{k, \omega}$-substructure, $\mathcal{L}_{k, \omega}$-equivalence, $\mathcal{L}_{\infty, \omega}$-substructure, for existentially universal structures      42Ч43
$\mathcal{L}_{k, \omega}$-equivalence, $\mathcal{L}_{k, \omega}$-substructure, $\mathcal{L}_{k, \omega}$-equivalence, $\mathcal{L}_{\infty, \omega}$-substructure, for regular models of arithmetic      162
$\mathcal{N}_D$      236 see second also
$\mathcal{N}_E$      168 see second also
$\mathcal{P}_{\Simga}$, $\mathcal{P}_T$      72Ч73 see also
Algebraically closed structures      1Ч2 13 15 224
Amalgamation of division algebras      196Ч197
Amalgamation property      50Ч51
Analytical hierarchy      117Ч131 184Ч186 241Ч252
Approximating chains      76Ч85
Approximating chains in arithmetic      182Ч186
Approximating chains in division algebras      244Ч247 250Ч252
Approximating chains, $\mathscr{H}$ chain      81Ч83 121Ч124 125Ч126
Approximating chains, $\varepsilon$ chain      83Ч85 121Ч124 125Ч126
Approximating chains, Cherlin chain      77Ч80
Approximating theories for $T^f$      104Ч110 124Ч125
Arithmetic, existentially complete models of      141 146Ч154 155Ч189
Arithmetic, existentially complete models of, Biregular models      140 165Ч170 172Ч178 179
Arithmetic, existentially complete models of, Existentially universal models      179Ч181
Arithmetic, existentially complete models of, Finitely generic models      188
Arithmetic, existentially complete models of, Infinitely generic models      179Ч181
Arithmetic, existentially complete models of, Regular models      6 139 160Ч165 168Ч172 180
Arithmetic, existentially complete models of, Simple models      6 139 155Ч159
Arithmetic, models of, Nonstandard      141
Arithmetic, models of, Standard      141
Arithmetic, second order, $\beta_n$-models      182Ч186
Arithmetic, second order, Interpretations of      168Ч169 236Ч240 241Ч252
Arithmetic, second order, Models of arithmetical comprehension      173Ч178
Arithmetic, second order, Structures for      168Ч186 233Ч236
Automorphisms of existentially complete division algebras      199Ч202 218Ч219
Automorphisms of existentially complete models of arithmetic      158 165
Center of a division ring      194
Centralizer in a division algebra      200Ч202 207Ч214 216Ч217
Characteristic of a division ring      194
Compactness Theorem      10
Complete type      41
Completeness theorem      10
Condition (for finite forcing)      87
Condition (for finite forcing), Complete sequence of conditions      96
d-prime ideals      225
d-radical ideals      227Ч228
d-radical of an ideal      225Ч227 228Ч231
Deduction Theorem      9
Definability in existentially complete structures, existentially defined subsets in arithmetic      160 162Ч163
Definability in existentially complete structures, of finitely generated division subalgebras      200
Definability in existentially complete structures, of N in existentially complete division algebras      233Ч235
Definability in existentially complete structures, of N in existentially complete models of arithmetic      151
Definability in existentially complete structures, of transcendental elements      203Ч204
Degrees of unsolvability      117Ч131
Degrees of unsolvability of $T^f$      124Ч125 241
Degrees of unsolvability of $xa(\mathcal{E}_n)$      121Ч124 125Ч126 184Ч186 244Ч247
Degrees of unsolvability of $xa(\mathcal{H}_n)$      121Ч124 125Ч126 184Ч186 244Ч247
Diagram of a structure      7
Division algebra      191Ч252
Division algebra, Existentially complete      195 198Ч222 240
Division algebra, Existentially complete, Embeddings of an      215Ч219
Division algebra, Existentially complete, Extensions of an      215Ч219
Division algebra, Existentially complete, Maximal subfields of an      207Ч214
Division algebra, Existentially complete, Subfields of an      202Ч206
Division algebra, Existentially universal      221 242Ч243
Division algebra, Finitely generated      219Ч222
Division algebra, Finitely generic      219 248Ч249
Division algebra, Finitely homogeneous      200 215Ч216
Division algebra, Infinitely generic      221 243Ч244
Division ring      193
Division ring, Existentially complete      195
Division ring, Existentially complete of characteristic 0 or p      195 (see division algebra also)
Elementary equivalence      9
Elementary extension      9
Elementary substructure      9
Enumeration Theorem (Kleene)      144
Existential closure (in arithmetic)      139 149 155
Existential completeness of a structure for a theory      17 22Ч28 31 48Ч50 59 69Ч73 77 81 96Ч98 111Ч115 121 129Ч131 132Ч136 141 146Ч154 155Ч189 195 198Ч222 240
Existential completeness of a structure in a class      16 19Ч21 59
Existential completeness of a structure in an extension      16 18
Existential type      29Ч43 65Ч69 72 112Ч115 127Ч128 156Ч157 161Ч163
Existential type of elements in a structure      30 39Ч43 65Ч69 72 156Ч157 161Ч163
Existential type, Defined in a structure      30
Existential type, Defined in a structure, Finite consistency of      33
Existential type, Defined in a structure, Finite satisfiability of      34
Existential type, Maximal existential type      30 39Ч40 41Ч43 112Ч115
Existential type, Realization of      30 155Ч156 161Ч163
Existentially universal structure      31 31Ч43 127Ч129 132Ч136 179Ч181 221 242Ч243
Forcing companions, Finite forcing companion      89Ч93 98Ч103 106Ч110 124Ч125 133 188 241 244 248Ч250
Forcing companions, Infinite forcing companion      70Ч71 119Ч124 125Ч129 131 133 180Ч181 243Ч244 248Ч250
Forcing, Finite forcing in model theory      87Ч110
Forcing, Finite forcing in model theory, by structures      93
Forcing, in set theory      4 55 86
Forcing, Infinite forcing in model theory      55Ч75
Forcing, Weak finite forcing      89
Forcing, Weak infinite forcing      71
Formula, $\exists_n$ formula      8
Formula, $\forall_n$ formula      8
Formula, Basic sentence      86
Formula, Defined in a structure      7
Formula, Existential formula      8
Formula, Prenex normal form for a      8
Formula, Primitive formula      3
Formula, Universal formula      8
Formula, Universal-existential formula      8
Formulas for arithmetic, $\Pi_n$ formula      141
Formulas for arithmetic, $\Sigma_n$ formula      141
Formulas for arithmetic, r.e. formula      142
Formulas for arithmetic, recursive formula      142
Generic structure, Finitely generic structure      93Ч100 101 103 108Ч110 111Ч112 132Ч136 188 219 248Ч249
Generic structure, Infinitely generic structure      56Ч64 69Ч73 79 80 82 84 111Ч115 131 132Ч136 179Ч181 221 243Ч244
Groups, Algebraically closed      2 5 16 53 195 222 251Ч252
Groups, Recursively presented      2 5
Henkin theory      119 120
Joint embedding property      52Ч54 70Ч71 101Ч102 125Ч129 133
Language of a structure      7
Matijasevic's Theorem      144 187 248
Model of a theory      8
Model which completes a theory      99Ч100 108Ч110
Model, Generalized elementary classes of models      8
Model, Inductive classes of models      9
Model-companion (of a theory)      3 69Ч72 100Ч103 133 134Ч136
Model-companion (of a theory), nonexistence for division algebras      206
Model-companion (of a theory), of an $\mathcal{N}_0$-categorical theory      115
Model-complete theory      3 45
Model-completeness for classes of structures      50 53 61Ч64 79Ч80 132
Model-completeness test for a theory      4 46
Model-completion of a theory      2Ч3 45 50Ч51 134Ч136
Model-consistency for classes of structures      50 53 61Ч64 79Ч80 132
Model-consistency for theories      44
Normal expansion of a language      86
Nullstellensatz for commutative fields      15Ч16 223
Nullstellensatz for division algebras      225Ч226
Obstructions to elementary extensions      81
Peano arithmetic      187Ч189
Persistent formula      77
Persistently complete structure      77
Persistently complete structure, $F_n$-persistently complete structures      83
Persistently complete structure, $\mathcal{H}_n$-persistently complete structures      81
Persistently complete structure, $\Sigma$-persistently complete structures      77
Polynomials, noncommutative      223Ч224
Pregeneric structure      72Ч75 135Ч136 150
Recursive functions, partial or total      142
Reduction Theorems for infinite forcing      66
Reduction Theorems for weak infinite forcing      72
Resultants for infinite forcing      65Ч68 69
Resultants for weak infinite forcing      72 112 114Ч115
Skew polynomial ring      196 210Ч213
Skew power series ring      196 210Ч212
Theory      8
Theory, $T_{\exists}, T_{\forall}, T_{\exists_n}, T_{\forall_n}$      8
Theory, $T_{\pi_2}$      141
Theory, $xa(M)$      9
Theory, $xa(M, \bar{m})$      9
Theory, $xa(\Sigma)$      9
Transcendental elements of a division algebra      199 202Ч204
Ultrapowers, recursively enumerable      156Ч157
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