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Ash C.J., Knight J., Sevenster A. (Ed) — Computable Structures and the Hyperarithmetical Hierarchy
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Название: Computable Structures and the Hyperarithmetical HierarchyАвторы: Ash C.J., Knight J., Sevenster A. (Ed)Аннотация: This book describes a program of research in computable structure theory. The goal is to find definability conditions corresponding to bounds on complexity which persist under isomorphism. The results apply to familiar kinds of structures (groups, fields, vector spaces, linear orderings Boolean algebras, Abelian p-groups, models of arithmetic). There are many interesting results already, but there are also many natural questions still to be answered. The book is self-contained in that it includes necessary background material from recursion theory (ordinal notations, the hyperarithmetical hierarchy) and model theory (infinitary formulas, consistency properties).
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 1st editionГод издания: 2000Количество страниц: 366Добавлена в каталог: 13.05.2008Операции: Положить на полку |
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Freeness, appropriate for 269 Freeness, appropriate for 264 Freeness, appropriate for intrinsically A relation 258 Freeness, notion appropriate for intrinsically 254 Friedberg 194 195 224 Friedberg — Muchnik Theorem 225 Function, non-computable 6 Games, in connection with ranks 99 General recursive 4 5 Generator for a principal type 47 202 Generator for complete type 202 Generic copy 161 163 164 167 175 176 309 Generic model representing a Scott set 309 Godel 4 5 52 292 319 Godel number vii 49 106 Godel — Rosser sentence 292 Godel’s Incompleteness Theorem 52 318 320 Goldbach’s conjecture 2 Goncharov vii 150 155 156 174 176 197 199 202 203 205—209 239 263 267 269 295 297 Groszek 214 Group vii 37 Group with solvable word problem 55 Group, computably presented 55 Group, finitely presented 55 Group, language of 36 Group, recursively presented 55 H(A) 71—75 81 85 H(a){X) 84 85 Halting set 12 320 Harizanov vii 166 188 189 195 Harrington 135 291 305—307 Harrison 129 248 Height in Abelian p-group 140 317 Height in tree 140 Height of element in well ordering 58 Henkin 45 48 Henkin construction 45 Hierarchy 24 Hierarchy, difference 86 Hierarchy, Ershov 86 Hierarchy, proper 24 78 hilbert 2 320 Hilbert’s 10th problem 2 3 6 52 319 320 Hird 195 Hirschfeldt 206 Homogeneity 45 47 Homogeneity of computable, or hyperarithmetical structure 126 Homogeneneity 202 Homogeneous 46 155 Homogeneous structure 137 Homogeneous structure, characterized by set of types 47 Hurlburt viii 284 Hyperarithmetical 71 74 80—83 Hyperarithmetical formulas 123 Hyperarithmetical hierarchy vi 71 74 75 85 87 184 239 263 Hyperarithmetical hierarchy, relativized 86 Hyperarithmetical infinitary formula vi Hyperarithmetical, relativized 84 Hyperarithmetically saturated 127—129 136 Independence of a formula 321 Independence of a sentence 321 Index for 79 Index for 79 Index for 77 Index for computable infinitary formula 106 Index for partial computable function 13 Index for Turing machine 5 Induction schema 318 Infinitary formula vi Infinitary formula, computable 90 Infinitary formulas, hyperarithmetical 116 Instruction function 214 215 228 231 265 266 270 279 Instruction function as source of high-level information 215 Instruction function, 236 Instruction function, 216 Instruction function, 218 219 Instruction function, 262 Interval algebra 131 150 247 250 272 282 316 Intrinsically 189 Intrinsically 253 Intrinsically 253 255 Intrinsically c.e. 181 183 Intrinsically c.e. relation, relatively 182 Intrinsically c.e., relatively 181 Intrinsically computable 181 185 Intrinsically computable, relation 198 Intrinsically computable, relatively 181 Intrinsically d-c.e. 189 Intrinsically d-c.e., relatively 167 Intrinsically, c.e. 182 Invariants, mathematical 143 Isomorphism 40 Isomorphism theorem 151 Isomorphism type 41 Jockusch 50 143 150—152 Jockusch and Soare 30 31 147 Jump 21 Jump, iterated 21 Jump, of a set 21 Jump, of a Turing degree 22 K 12 18 21 22 27 29 Kaplansky 317 Kaye 318 Keisler 48 89 124 312 Keisler, method of expansions 124 Khisamiev 139 Khoussainov 206 Kleene 4 13 24 57 61 62 67 74 78 82 84 131 227 Kleene symposium 213 Kleene — Brouwer ordering 82 131 Kleene’s normal form theorem 8 Konig’s lemma 30 Kontostathis 214 Koppelberg 315 Kreisel vi 121 123 Kripke 123 Kripke — Platek set theory vi 123 Kudinov 206 Kueker 101 l-free 189 190 267 Lachlan 309 Language, computable 49 Language, infinitary, predicate 89 Language, infinitary, propositional 89 Language, of groups 36 Language, of orderings 36 Language, predicate 33 34 Language, predicate, first order 33 Language, propositional 33 Lattice of c.e. sets 55 135 Least, or 8 Left limit 277 Lempp 152 155 214 Lerman viii 145 214 297 309 Limit Lemma 28 Linear dependence, formula defining 90 Linear ordering vii 33 37 160 173 206 208 244 282—284 287 311 314 316 Linear ordering as algebra 287 Linear ordering of type 276 Linear ordering of type 276 Linear ordering of type 277 Linear ordering, dense, without endpoints 41 Linear ordering, language of 36 Logical connective 33 Logical connectives 34 Logical constant 33 logical constants 34 Logical quantifiers 34 Logically equivalent 34 40 Love 143 150 209 210 Low 22 30 53 151 306 307 Low Basis Theorem 30 50 Lowenheim — Skolem theorem 44 Lowenheim — Skolem Theorem for infinitary logic 94 Makkai 94 95 101 136 Manasse 160 185 Many-one, degree 17 Many-one, equivalence 17 Many-one, reducibility 17 Marker 54 291 295 296 307 309 Matijasevic 7 52 308 319 320 McAllister viii 309 McAloon 291 305 McCoy viii 167 169 176 178 201 McNicholl, ix 167 169 Metakides 177 187 Metatheorem 213 235 237 252 Metatheorem for 213 Metatheorem for finite-injury priority constructions 224 Metatheorem for priority construction 227 Metatheorem for priority constructions vi 133 Metatheorem, transfinite 227 Method of workers 291 Michalski viii 224—226 Millar 155 Minimal upper bound for set of degrees 309 Miranda viii Model of a sentence, or set of sentences 39 Monk 315 Morley 155 213 Muchnik 194 195 224 Mytilinaios 214 n-c.e. 86 167 n-system 215 220—223 227 228 Nadel 294 Nerode 159 177 181 182 187 198 239 Normal form 94 102 105 107 Normal form for analytical relation 76 Normal form in infinitary logic 93 Normal Form Theorem 94 Normal form, prenex 40 Novikov 55 Nurtazin vii 201 206 o 57 61 62 64—67 71 82 O, path through 66 O-minimal 313 Oates viii 140 Object of 215 Object of priority construction, mathematical formulation 214 Odintsov 289 Omitting a type 48 Operations on linear orderings 59 Operations on ordinals 59 Oracle 14 Oracle machine 15—17 Order type 58 59 61 63—66 68 69 314 Ordering and hyperarithmetical automorphisms 131 Ordering of type 218 Ordering of type 198 Ordering of type 182 192 Ordering of type 219 Ordering of type 181 197 Ordinal 57 Ordinal notation vi 71 227 Ordinal, classification 58 Ordinal, computable 61 Ordinal, constructive 62 Ordinal, countable 58 Ordinal, least non-constructive 62 Ordinal, limit 58 Ordinal, non-computable, existence of 61 Ordinal, notation for 61 Ordinal, set theoretic definition 58 Ordinal, successor 58 Ordinal, uncountable, existence of 58 Ordinal, X-computable 119 Overspill 53 293 297 318 PA 53 137 291 292 296 297 303 306 307 318—321 PA, axioms for 318 PA, completion of 22 54 291—297 306—309 319 321 PA, nonstandard model of 53 291 293 294 296 297 306 307 309 318 319 Pairing function 7 Partial ordering 314 Partial ordering, strict 314 Partition of Boolean algebra 246 Path, through tree 215 Peano arithmetic, first order 318 Peretyat’kin 155 156 202 295 297 Picture 230 235 Picture in proof of metatheorem 223 Picture, completing 230 Picture, completion of 223 Platek 123 Prenex normal form 40 Presburger arithmetic 56 Presentation, group 42 Prime 155 Prime model 47 201 202 Prime model, decidable 202 Primitive recursive 5 Principal type 201 Priority conjstruction, object 213 Priority construction 121 133 213 Priority construction, 213 227 Priority construction, vi Priority construction, abstract statement of object 215 Priority construction, finite injury 181 199 Priority construction, finite-injury vi 184 213 216 Priority construction, general features 213 Priority construction, infinite-injury 213 Product of orderings 59 315 Product of ordinals 59 60 proof 42 44 Proper hierachy 75 Propositional structure 34 Propositional variables 33 Quantifier elimination 242 Quantifier-free 312 Quantifiers 34 Quasi-simple 195 Quotient algebra 150 210 Quotient algebra, 284 Quotient algebra, c.e. 284 288 Quotient group 42 56 Quotient order 287 Quotient ordering 42 143 216 287 Quotient structure 33 41 43 55 56 143 209 275 287 Quotient structure, 111 Quotient structure, 55 Quotient structure, 111 Quotient structure, 287 Quotient structure, 55 Quotient structure, 111 Quotient structure, c.e. 55 110 210 Quotient structure, complexity of 55 Quotient structures, 111 Quotient, structure 42 r.e. 5 Rank 136 247 Rank of 250 Rank of 250 Rank of 248 Rank of 248 Rank of 248 rank, calculating 239 Rank, examples 100 Rank, R 98 Rank, SR 98 Real closed field 187 Recursion theorem 13 14 64 67
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