Fenstad J.E. — General recursion theory: An axiomatic approach :: Электронная библиотека попечительского совета мехмата МГУ

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Fenstad J.E. — General recursion theory: An axiomatic approach

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Название: General recursion theory: An axiomatic approach

Автор: Fenstad J.E.

Аннотация:

This book has developed over a number of years. The aim has been to give a unified and coherent account of the many and various parts of general recursion theory. I have not worked alone. The Recursion Theory Seminar in Oslo has for a number of years been a meeting place for an active group of younger people. Their work and enthusiasm have been an important part of the present project. I am happy to acknowledge my debts to Johan Moldestad, Dag Normann, Viggo Stoltenberg-Hansen and John Tucker. It has been a great joy for me to work together with them.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1980

Количество страниц: 244

Добавлена в каталог: 19.11.2013

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Предметный указатель

Aanderaa, S. [1]      83 85
Abstract 1-section      135
Acceptable structure      87
Aczel, P. [2]      42
Aczel, P. [3]      67 82 83
Aczel, P. [4]      79 82
Aczel, P. [5]      124
Aczel, P. [6]      79 82
Aczel, P. [7]      79
Aczel, P., Aczel, Hinman [8]      204
Aczel, P., Richter, Aczed [135]      83
Adequate      144 158
Admissibility in set-recursion      187 188
Admissible collapse      163
Admissible ordinal      109 137 160
Admissible ordinal, $\Theta$ -admissible      129
Admissible ordinal, F-admissible      130
Admissible ordinal, next-admissible      124 125
Admissible prewellordering      110 113
Admissible set      109
Admissible set, next admissible      124 125
Admissible set, non-transitive      29
Associate      205
Barendregt, H. [9]      203
Barwise, K.J.      81
Barwise, K.J. [10]      124
Barwise, K.J. [11]      82 109 110 126
Barwise, K.J. [13]      82
Barwise, K.J., Barwise, Gandy, Moschovakis [14]      124
Basis results      204
Bergstra, J. [15]      139 207
Blocking procedure      153
Cenzer, D. [18]      83
Characterization theorem, admissible prewellorderings      121
Characterization theorem, normal theories      180
Characterization theorem, Spector theories      129
Code set      20
Coding scheme      90
Computation domain      19 30 90 111
Computation set      20
Computation structure      44
Computation theory      8 44
Computation theory, $\Theta$ -Mahlo      128 180
Computation theory, $\Theta$ -resolvable      111
Computation theory, equivalence of      34 48 76
Computation theory, extension      34 48
Computation theory, infinite      112
Computation theory, normal      168
Computation theory, p-normal      66
Computation theory, precomputation      22 30
Computation theory, regular      52
Computation theory, s-normal      58
Computation theory, set-recursion      183
Computation, convergent      94
Computation, derivation      57
Computation, deterministic      57
Computation, divergent      94
Computation, immediate subcomputation      32 47 94
Computation, length of computation      32 44 46 65 94 183
Computation, subcomputation      32 38 44 47 54 57 94 183
Computation, subcomputation tree      33 38 95 183
Continuous functional      204
Countable functional      204
Countable functional, associate      205
Countable functional, fan functional      206
Countable functional, Kleene computable      206
Countable functional, recursively countable      206
Cut-elimination lemma      57
Deficiency set      148
Definition by cases      21
Degree      140 150 157
Density theorem      157
Descriptive set theory      79 203
Determinacy      158
Devlin, K.J. [19]      182 183
Diagonalization operator for inductive definitions      204
Driscoll, G.C., Jr. [21]      145
Effective discontinuity      205
Enumeration, $\preceq$ enumeration      141
Enumeration, enumeration property      13
Envelope      73 171
Envelope, extended      73
Envelope, S-envelope      171
Ershov, Y.L. [22]      207
Ershov, Y.L. [23]      207
Faithful representation theorem      58
Fap C-computable      6
Fap CS-computable      6
Fap S-computable      5
Fap-computable      4
Fattening lemma      127 180
Feferman, S. [24]      136
Feferman, S. [25]      12 14 207
Fenstad, J.E. [26]      15 124
Fenstad, J.E. [27]      15
Fenstad, J.E. [28]      15
Fenstad, J.E. [29]      15
Fenstad, Normann [32]      203
Finite, $\beta$ -finite      159
Finite, $\Theta$ -finite      52 66
Finite, invariantly finite      162
Finite, strongly $\Theta$ -finite      66
Finite, weakly $\Theta$ -finite      66
First recursion theorem      40 48 75 95
Fixed-point operator      7 11
Fixed-point property      13
Fixed-point theorem      25
Forcing      137
Friedman, H. [33]      3 42
Friedman, H. [34]      4 5
Friedman, S.D. [35]      159 160
Friedman, S.D. [36]      160
Friedman, Sacks [31]      159
Function, $\Theta$ -computable      21
Function, partial multiple-valued (pmv)      20
Functional, composition      22
Functional, consistent      21
Functional, monotone      13 95
Functional, partial multiple-valued (pmv)      21
Functional, partial recursive      95
Functional, permutation      22
Functional, strongly $\Theta$ -computable      39
Functional, uniformly weakly $\Theta$ -computable      46
Functional, weakly $\Theta$ -computable      21 44
Functional, weakly partial recursive      95
Gandy fixed-point theorem      110
Gandy selection theorem (3.1.6)      65 68
Gandy — Spector theorem      99 123 190 191
Gandy, R.O. [38]      65 204
Gandy, R.O. [39]      79 80
Gandy, R.O. [40]      182
Gandy, R.O., Barwise, Gandy, Moschovakis [41]      124
Gandy, R.O., Gandy, Hyland [42]      207
Gandy, R.O., Gandy, Sacks [43]      136
Gap phenomena      204
Gordon, C.E. [45]      110
Gregory, J. [46]      109
Grilliot selection theorem      90 100 184
Grilliot, T.J. [48]      100
Grilliot, T.J. [49]      80 83 87 88
Grilliot, T.J. [50]      205
Grilliot, T.J. [51]      203
Gurrik, P.K. [52]      183 189
Harrington, L.A.      77 79 158 204
Harrington, L.A. [53]      169 171 182 190 194 202 204
Harrington, L.A. [54]      204
Harrington, L.A., Harrington, Kechris [56]      134
Harrington, L.A., Harrington, Kechris [57]      83 87
Harrington, L.A., Harrington, Kechris, Simpson [58]      134
Harrington, L.A., Harrington, MacQueen [55]      90 100

Hereditarily consistent functionals      11
hierarchies      204
Hinman, P.G. [59]      67
Hinman, P.G. [60]      207
Hinman, P.G. [61]      204
Hinman, P.G., Aczel, Hinman [8]      204
Hinman, P.G., Hinman, Moschovakis [62]      181
Hodges, W. [63]      203
Hyland, J.M.E. [64]      207
Hyland, J.M.E. [65]      207
Hyland, J.M.E. [66]      207
Hyland, J.M.E. [67]      207
Hyland, J.M.E., Gandy, Hyland [42]      207
Hyperanalytic      90
Hyperprojective theory      181
Hyperregular      146
Imbedding theorem      126
Inadmissible ordinal, strongly      160
Inadmissible ordinal, weakly      160
Inadmissible theory      159
Induction algebra      14
Inductive definability      7 79
Inductive definability, $\prod^{0}_{1}$       80
Inductive definability, $\prod^{1}_{1}$ monotone      81
Inductive definability, $\sum^{0}_{2}$       87
Inductive definability, $\sum^{1}_{1}$ monotone      82
Inductive definability, fixed-points of      79
Inductive definability, monotone      79
Inductive definability, ordinal of      79
Inductive definability, positive $\sum^{0}_{1}$       80
Inductive definability, positive elementary      81
Inductive definability, stages of      79
Inductive relations, C-coinductive      80
Inductive relations, C-hyperdefinable      80
Inductive relations, C-inductive      80
Infinite computation theory      112
Iteration property      22 45
Jensen, R.B. [70]      136
Jensen, R.B. [71]      182 183
Jensen, R.B., Jensen, Karp [72]      109 182
Jump      149
Jump, a-jump      195
Karp, C., Jensen, Karp [72]      109 182
Kechris, A.S. [74]      134 169 190 204
Kechris, A.S. [75]      79
Kechris, A.S. [76]      106 169 203 204
Kechris, A.S., Harrington, Kechris [56]      134
Kechris, A.S., Harrington, Kechris [57]      83 87
Kechris, A.S., Harrington, Kechris, Simpson [58]      134
Kechris, A.S., Kechris, Moschovakis [77]      12 13
Kierstead, D.P.      203
Kleene recursion in higher types (S1-S9)      67 106
Kleene recursion in higher types (S1-S9) and set-recursion      189 192
Kleene, S.C. [78]      41
Kleene, S.C. [79]      65 122
Kleene, S.C. [80]      65 122
Kleene, S.C. [81]      65 122
Kleene, S.C. [82]      207
Kleene, S.C. [83]      3 42 65 67 94 206
Kleene, S.C. [84]      123
Kleene, S.C. [86]      203
Kolaitis, P.G. [87]      82
Kreisel, G. [88]      207
Kreisel, G. [89]      52 65
Kreisel, G. [90]      145
Kreisel, Sacks [91]      52 65 123
Kripke, S.      109
Kripke, S. [92]      123
Lambda-calculus      42 203
Lavori, P. [95]      204
Locally of type I      188
Louveau, A. [96]      203
Louveau, A. [97]      203
Maass, W. [100]      160 163
Maass, W. [101]      159
Maass, W. [102]      161 163
MacQueen, D.B. [98]      100 182 190
MacQueen, D.B., Harrington, MacQueen [55]      90 100
Malcev, A.I. [99]      10
Mapping      21
Minimum operator ( $\mu$ -operator)      27
Mitschke, G. [104]      203
Moldestad, J.      60
Moldestad, J. [105]      7 11 90 99 100 106 134 135 168 169 171 203 204
Moldestad, J. [106]      29
Moldestad, J., Moldestad, Normann [107]      204
Moldestad, J., Moldestad, Stoltenberg-Hansen, Tucker [108]      4 5 6 8
Moldestad, J., Moldestad, Stoltenberg-Hansen, Tucker [109]      4 6 9
Moldestad, Tucker [110]      14
Moschovakis, Y.N.      182
Moschovakis, Y.N. [111]      90
Moschovakis, Y.N. [112]      3 42 110 124
Moschovakis, Y.N. [113]      3 42 43 46 48 52 65 72 110 121 122
Moschovakis, Y.N. [114]      75 90
Moschovakis, Y.N. [115]      74 79 81 82 87 124
Moschovakis, Y.N. [116]      79 83 84
Moschovakis, Y.N. [117]      12 14 79
Moschovakis, Y.N. [118]      79 106 203
Moschovakis, Y.N., Barwise, Gandy, Moschovakis [14]      124
Moschovakis, Y.N., Hinman, Moschovakis [62]      181
Moschovakis, Y.N., Kechris, Moschovakis [77]      12 13
Normal function      130
Normal list      97
Normal type-2 functional      127
Normann, D.      184 202
Normann, D. [121]      137
Normann, D. [122]      182 190
Normann, D. [123]      207
Normann, D. [124]      182 184 189
Normann, D. [125]      202
Normann, D. [126]      204
Normann, D. [127]      202
Normann, D. [128]      207
Normann, D. [129]      207
Normann, D., Fenstad, Normann [32]      203
Normann, D., Moldestad, Normann [107]      204
Normann, D., Normann, Stoltenberg-Hansen [130]      158
Normann, D., Normann, Wainer [131]      207
Nyberg, A. [132]      110
Operator, $\Theta$ -computable      84
Operator, adequate class      87
Operator, typical non-monotone class      83
Ordered n-tuple      31
Ordinal, $\Theta$ -Mahlo      130
Ordinal, subconstructive      172
p-normal      66
Pairing structure      30
Parametrization, $\omega$ -parametrization      13
Parametrization, $\preceq$ -parametrization      141
Parametrization, Spector classes      74
Partial recursive function      93 94
Platek, R.A.      109
Platek, R.A. [133]      7 11 124
Plus-one theorem      138
Plus-two theorem      171
Post, E.      80
Precomputation theory      22 30
Predecessor function      27
Prewellordering      65 85
Prewellordering, length of      111
Prime computable      3
Prime computation set      32 46
Primitive recursion      28 91
Primitive recursive set function      182
Priority argument      140 156 182 202
Projectible      142
Projectum      143
Projectum, r.e.-projectum      144
Quantifier, Monotone      67 82
Reducibility relations      140

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