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Abramsky S., Barwise J., Fine K. — Recursive Functionals. Studies in Logic and the Foundations of Mathematics Volume 131
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Название: Recursive Functionals. Studies in Logic and the Foundations of Mathematics Volume 131
Авторы: Abramsky S., Barwise J., Fine K.
Аннотация: This work is a self-contained elementary exposition of the theory of recursive functionals, that also includes a number of advanced results. Although aiming basically at a theory of higher order computability, attention is restricted to second order functionals, where the arguments are numerical functions and the values, when defined, are natural numbers. This theory is somewhat special, for to some extent it can be reduced to first order theory, but when properly extended and relativized it requires the full machinery of higher order computations. In the theory of recursive monotonic functionals the author formulates a reasonable notion of computation which provides the right frame for what appears to be a convincing form of the extended Church's thesis. At the same time, the theory provides sufficient room to formulate the classical results that are usually derived in terms of singular functionals. Presented are complete proofs of Gandy's selector theorem, Kleene's theorem on hyperarithmetical predicates, and Grilliot's theorem on effectively discontinuous functionals.
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Рубрика: Математика /
Статус предметного указателя: Готов указатель с номерами страниц
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Год издания: 1992
Количество страниц: 279
Добавлена в каталог: 13.08.2015
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Предметный указатель
Abstraction 161
Algorithm 86 181
Algorithm, deterministic 74
Algorithm, explicit 50 86
Algorithm, recursive 110
Analytic 243
Anti-symmetric 5
Application 1
Application, functional 37
ASSIGNMENT 129
BASIC 37
Basic functional 37
Basic operation 39
Basic, primitive recursion 52
Basic, recursive term 69
Basic, term 47
Boolean 20
Boolean, extension 23
Boolean, monotonic 23
Boolean, values 20
Bottom 6
Bounded 56
Bounded minimalization 58
Bounded product 57
Bounded quantification 60
Bounded sum 56
CALL 111
Call, direct 113
Call, indirect 114
Cartesian product 19
cases 38
Cases, definition 38
Cases, general 40
Characteristic functional 25 35
Characteristic functional, dual 25 35
Characteristic functional, partial 25 35
Church's thesis 67 88
Closed 128
Coenumerable 193
Cohyperenumerable 236
complete 17 229
Computable 36
Computable, recursively 117
Computation 86 110
Computation rules 86 110
Condition 4
Condition, inductive 251
Condition, single-valued 4
Condition, total 4
Configuration 86 110
Conjunction 21 24
Consistent 7 172 227
Consistent, set 7
Constant functional 37
continuous 206
Cover 142
Definable 136
Definable, formally 136
defined 1
Defined mapping 1
Defined well 4
Definition 3
Definition, mapping 3
Definition, predicate 26
Deflector 210
Denotation 129
Discontinuous 209
Discontinuous, effectively 213
Discrete 5
Discrete poset 5
Disjunction 21
distribution 38
Distribution, predicate 42
Domain 8
Dual 26 35
Effectively discontinuous 213
Elemental 243
Enumerable 193 197
Existential quantification 19
Existential quantification, barred 234
Existential quantification, bounded 50
Existential quantification, functional 233
Existential quantification, unbounded 190
Explicit 3
Explicit algorithm 50
Explicit specification 3 50
Extension 4
Extension, Boolean 23
Extension, mapping 4
Factorization 209
Fenstad, J.E. 14 170
Fixed point 9
Formalization 125
Formalization, closed 128
Formalization, language 126
Formalization, linear 128
Formalization, regular 128
Formalization, term 126
Formalization, variable 126
Function 30
Function, number decoding 59
Function, number encoding 59
Functional 16 30
Functional application 37
Functional characteristic 26
Functional complete 17
Functional constant 37
Functional discontinuous 209
Functional effectively discontinuous 213
Functional preorder 165
Functional primitive recursive 54
Functional projection 37
Functional singular 18
Functional successor 51
Functional, continuous 206
Functional, quasi-total 17 55
Functional, recursive 110
Functional, similar 18
Functional, weakly normal 213
Gandy, R.O. 124 232
Graph predicate 26 35
Greatest lower bound 8
Grilliot, T.J. 205 206 211 212 217
Hindley, J.R. 139 156
Hinman, P.G. 14 45 170 187 217 232 258
Hyperarithmetical 239
Hyperenumerable 235 239
Inconsistent 7
INDEX 159 174
Induction 251
Inductive 251
Interpreter 158
Intersection 34
Jump 184
Kechris, A.S. 108 124
Kleene, S.C. 45 95 187 200 217 242 258 260
Kreisel, G. 217
Least upper bound 7
Linear 128
Lower bound 6
Lower bound, greatest 8
machine 111
Mapping 1
Mapping, assignment 129
Mapping, defined 1
Mapping, definition 3
Mapping, monotonic 15
Mapping, partial 2
Mapping, specification 2
Mapping, total 2
Mapping, undefined 1
Maximal 6
Minimal fixed point 10
Minimalization 58 68
Minimalization, bounded 58
Minimalization, unbounded 68
Moldestad, J. 124
Monotonic 15
Monotonic boolean 23
Monotonic extension 23
Moschovakis, Y.N. 108 124 258
Negation 21 24
normal 231
Normal, weakly 213
Norman, D. 217
numerical 30
Numerical function 30
Numerical predicate 34
Numerical substitution 37 40
Operations 39
Operations, -recursive 68
Operations, basic 39
Operations, primitive recursive 52
Operations, recursive 110
Oracle 112
Partial characteristic functional 25 35
Partial ordered set 5
Partial ordering 5
Platek, R.A. 124
Point 9
Point, minimal fixed 9
Polish normal form 75
POSET 5
Poset, discrete 5
Predicate 22 33
Predicate, coenumerable 193
Predicate, distribution 42
Predicate, enumerable 193
Predicate, numerical 34
Predicate, partially recursive 192
Predicate, primitive recursive 192
Predicate, recursive 192
Prefix 127
Prefix, -prefix 127
Prefix, -prefix 127
Preorder functional 165
Preordered 168
Prime number enumeration 58
Primitive recursion 51
Primitive recursion, basic 52
Projection functional 37
Quantifier 21
Quantifier, barred 234
Quantifier, bounded 60
Quantifier, unbounded 190
Quasi-similar 153
Quasi-total 17
RANGE 27
Recursion 51
Recursion, basic 71
Recursion, functional 102
Recursion, operational 110
Recursion, primitive 51
Recursion, simultaneous 106
RECURSIVE 69
Recursive algorithm 110
recursive call 77
Recursive Functional 110
Recursive machine 112
Recursive operation 110
Reflexive structure 158
Regular 6
Regular element 6
Regular poset 6
Regular set 149
Regular, term 101
Representation 172
Restriction assumption 145
Rogers, H. 242
Sanchis, L.E. 13 29 47 58 67 69 71 84 89 95 162 167 170 187 189 232 258
Seldin, J.P. 139 156
Selector property 168
Semantics 127
Semantics, reductional 127
Semantics, structural 127 131
Similar 18
Similar extension 191 240
Single-valued 4
singular 17
Specification 2
Specification, explicit 3
Specification, mapping 2
Specification, relational 3
STACK 74
Stack, algorithm 74
Structure 158
Substitution 37
Substitution, formal 134
Substitution, free 134
Substitution, functional 62
Substitution, numerical 37
Substitution, predicate 43
Support 113
system 110
Term 47
Term, analytic 243
Term, basic 47
Term, elemental 243
Term, functional 98
Term, inductive 251
Term, regular 251
Top 6
total 2
Total condition 4
Total mapping 2
Tourlakis, G.J. 45 124 187
Transformation 9 70
Tugue, T. 187
Tuples 31
Type-(k,m) 126
Type-0 29
Type-1 126
Type-1, functional 126
Type-1, numerical 126
Type-k 126
union 34
Universal quantification 19
Universal quantification, barred 234
Universal quantification, bounded 49
Universal quantification, functional 233
Universal quantification, unbounded 190
Upper bound 6
Variable 126
Variable, bound 128
Variable, formal 126
Variable, free 128
Variable, renamed 145
Variable, renaming 145
Variant 146
Weakly normal 213
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