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Abramsky S., Barwise J., Fine K. — Recursive Functionals. Studies in Logic and the Foundations of Mathematics Volume 131
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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 279

Добавлена в каталог: 13.08.2015

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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, $\mu$-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, $\Lambda$-prefix      127
Prefix, $\mu$-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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