Smullyan R.M. — Recursion Theory for Metamathematics :: Электронная библиотека попечительского совета мехмата МГУ

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Smullyan R.M. — Recursion Theory for Metamathematics

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Название: Recursion Theory for Metamathematics

Автор: Smullyan R.M.

Аннотация:

This work is a sequel to the author's Godel's Incompleteness Theorems, though it can be read independently by anyone familiar with Godel's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 163

Добавлена в каталог: 29.11.2009

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Предметный указатель

$E[\overline{a}_{1},...,\overline{a}_{n}]$       36
$F[\overline{n}]$ and $F(\overline{n})$       2
$J_{n}(x_{1},...,x_{n})$       34
$K^{n}_{i}$       35
$P^{\sharp}$       21
$R^{\sharp}$       21
$\omega$ -consistent      5
$\omega$ -inconsistent      5
$\sum_{0}$ -complete      11
$\sum_{0}$ -formulas      9
$\sum_{0}$ -relations      9
$\sum_{1}$ -formula      9
$\sum_{1}$ -relation      9
A*      2
Admissible functions      19
Arithmetic      9
Associate      139
Axiomatizable systems      11
Bar symmetric recursion theorem      116
Bounded quantifiers      9
co-productive      59
complete      3
Complete E.I. function      68
Complete effective inseparability      68
Complete productivity      59
Complete set      59
Completely creative      59
Completely creative function      59
Completely creative set      59
Completely E.I.      68
Completely E.I. systems      72
Completely productive      59
Completely productive function      59
Constructive arithmetic      9
Constructive arithmetic relation      9
Creative sets      58
Creative systems      58
D(X)      2
D.G.      78
D.G. function      78
D.U.      76
Decidable      39
Decision procedure      39
Diagonal function      2
Double analogue of Myhill's fixed point theorem      110
Double generativity      78
Double master functions      112
Double productivity      113
Double recursion theorems      107
Double recursion with a pairing function      112
Double sentential recursion property      145
Double universality      76
Doubly co-productive      124
Doubly generative      78
Doubly generative pairs      78
Doubly generative relative to      87
Doubly universal      76
DSR      145
E.I.      68
E.I. function      68
Effective Rosser systems      73
Effective separation      56
Effectively a Rosser system      73
Effectively an exact Rosser system      75
Effectively DSR      148
Effectively Goedelian      144
Effectively inseparable      68
Effectively semi-DSR      149
Effectively SR      149
Enumerable in $\mathcal{S}$       5
Enumeration theorem      48
Essential undecidability      42
Essentially undecidable      42
Exact Rosser fixed point property      150
Exact Rosser function      75
Exact Rosser system      20
Exact separation      8
Exactly separates      8
Existential quantification      26
Explicit definability      25
Explicitly definable      25
Express      9
Extended recursion theorem      105
Extension      12
Feebly co-productive      139
Feebly D.G.      141
Feebly doubly co-productive      141
Feebly generative      139
Finite existential quantification      26
Finite quantifications      26
Finite universal quantification      26
G.I.T.      1
Generative function      59
Generative relative to      84
Generative sets      59
Goedel numbering      2
Goedel sentence      3
Goedel — Rosser incompleteness theorem      16
Goedelian systems      144
incomplete      3

Indexing      48
Iteration theorem      51
Iterative function      60
J(x,y)      31
Kleene function      69
Kleene's symmetric form of Goedel's theorem      70
Kx      31
Lemma $\omega$       6
lx      31
Many-one reducibility      60
Many-one reducible      60
Master functions      55
Maximal indexing      54
Myhill's fixed point theorem      103
Negative Goedel sentence      3
P      2
Post's sets C and K      58
Productive      58
Productive function      58
Productive set      58
Pseudo-uniform reducibility      137
Pseudo-uniform reducibility for pairs      137
Pseudo-uniformly reducible      137
R      2
r(a,b)      2
r.e. indexing      54
R.I.      44
R.I. system      44
Recursion theorems      96
Recursive inseparability      43
Recursive pairing functions      31
Recursive relations      10 27
Recursively axiomatizable      11
Recursively enumerable      10
Recursively inseparable      43
Recursively separable      43
Reducibility      71
Reducible      60 71
Reduction      71
Regular relations      30
Represent      3
Representability      3
Rice's theorem      99
Rosser fixed-point properties      150
Rosser function      73
Rosser system      12
Rosser system for sets      12
Rosser systems      12
Semi-D.G. function      80
Semi-D.G. pairs      80
Semi-D.U.      76
Semi-double sentential recursion property      145
Semi-DSR      145
Semi-DSR systems      145
Semi-reducibility      71
Semi-reducible      72
Semi-reduction      71 88
Sentential double generativity      81
Sentential recursion property      143
Sententially D.G.      82
Sententially generative      64
Separability      7
Shepherdson's exact separation lemma      21
Shepherdson's representation lemma      20
Simply consistent      3
Strong double recursion theorem      109
Strong recursion theorem      100
Strongly separates      7
Subsystem      12
Superset      7
Symmetric form of Goedel's theorem      70
Symmetric recursion theorem      111
Tarski's theorem      16
The enumeration theorem      49
Three incompleteness proofs for Peano arithmetic      16
Undecidable      3 39
Undecidable systems      39
Uniform Goedelization      143
Uniform incompletability      143
Uniform iteration theorem      54
Uniform reducibility      131
Uniform reducibility for pairs      133
Uniform representability      62 63
Uniform universality      61
Uniformly definable      131
Uniformly incompleteable      143
Uniformly reducible      131
Uniformly representable      62 130
Uniformly universal      61
Universal      60
Universal quantification      26
Universal sets      60
Unsolvable problems      98
Weak double Myhill theorem      108
Weak double productivity      124
Weak double recursion theorem      107
Weak productivity      122
Weak recursion theorem      97
Weakly co-productive      122
Weakly co-productive under g(x)      122
Weakly E.I.      127

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