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Epstein R.L. — Degrees of Unsolvability: Structure and Theory
Epstein R.L. — Degrees of Unsolvability: Structure and Theory

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Название: Degrees of Unsolvability: Structure and Theory

Автор: Epstein R.L.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1979

Количество страниц: 240

Добавлена в каталог: 14.08.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C_{A}$-domination Theorem      154
$Low_{1}$      156
$Low_{2}$      160ff
$\mathfrak{F}$-r.e      197
$\mu$-operator      2
$\omega^{th}$-jump      126
Agree on the evens      49
Agree on the odds      35
Agree on X      53
Algorithmic class of functions      2
Analysis      116
Analysis, $\underline{a}$-      170
Approximation, recursive      13
Arithmetic      116
Arithmetical degree      14
Arithmetical set      14
atom      191
Automorphism basis      207
Boolean lattice      190
Boolean lattice, generaled by      190
Bottomed      27
Branching      16
Case Defining Lemma      49 68
Chain      190
Characteristic function      2
Church’s thesis      2
Compactness of functionals      8
Compatible strings      5
Compatible strings on the odds      35
Complement      189
Complement, relative      189
Complete r.e. set      12
Computation      3
Computation in time s      4
Computation Lemma      57
Computation Lemma (on the Odds)      39
Computation Lemma (recursive case)      18
Correspondence Corollary      173
Cover      188
Cover, minimal      34
De Morgan’s Identities      189
Definable a is, in arithmetic      184
Definable in $\mathfrak{DJ}$      116
Definable in $\mathfrak{D}$      116
Definable in Analysis      116 130
Definable with parameters in $\mathfrak{D}$      132
Defined at stage s      11
Defining pair for level of a tree      37
Degree of unsolvability      9
Diagonalization lemma      56 (see also “Posner’s Lemma”)
Diagonalization Lemma (recursive case)      54
Diagonalization Lemma (weak form)      55
diamond      48
Distributive lattice      187
Distributive lattice of specified degree      106ff
Dominates, function      154
Double Limit Lemma      91
Exact pair      118
Extension on a tree      16
f-r.e      153 197 210
Finite injury      147
Forces the jump      139 140
Forces the jump, relative to a tree      140
Full approximation construction      145 162
Full subtree above      17
Full tree      17
Fully uniform tree      37
Functional, partial recursive      6
Functional, partial recursive, compactness of      8
Functional, partial recursive, consistency condition      6
Functional, partial recursive, standard enumeration of      7
High degree      157ff
High set      159
Homogeneity conjecture      31 234
Homogeneity conjecture, strong      32 106 202 229
Hugill’s conditions      227
Ideal of degrees      117
Ideal of degrees, Characterization of      117
Identity tree      15
Incompatible strings      5
Index for a p.r. function      4
Index for a p.r. functional      8
Infinite injury      91ff
Initial segment of degrees      27
Interval in a lattice      189
Introreducible set      141
Join      187
Join-irreducible      190
Jump of A      10
Jump, $n^{th}$-      10
Jump, $\omega^{th}$-      126
Jump, forces the      139 140
Jump, operator      10
Jumps and Chains Theorem      103
Kleene T-predicate      3
Lattice      187
Lattice, bottomed      27
Lattice, distributive      187
Lattice, homomorphism      187
Lattice, sub-      187
Lattice, topped      74
Lattice, upper-semi-      187
Least search operator ($\mu$)      2
Length of a string      5
Lies on a tree      16
Lies on a tree, above      16
Lies on a tree, below      16
Limit Lemma      13
Limit of functions      11
Meet      187
Meet-irreducible      190
Miller & Martin’s Lemma      154
Minimal cover      34
Minimal degree      20
n-minimal over      133
n-r.e. degree      153 195ff 210
n-r.e. set      152
Node of a tree      16
Node of a tree, S-O      42
Normal Form Theorem      3
Odds, the, agree on      35
Odds, the, compatible on      35
Odds, the, part of      34
Odds, the, Special on      35
Order Reversing Correspondence      120
Ordering of strings      6
O’-oracle construction      162
Pairing function      3
Partial recursive (p.r.) function      3
Partial recursive (p.r.) functional      6
Partial recursive (p.r.) functions in A      3
Partial recursive (p.r.) tree      17
Partition Representation Theorem      191ff
Passes through, a string      16
Perfect closed set      230
Permitting argument      145ff 163
Posner’s Lemma      19 201
Power set of X      188
Presentable, a-      88
Primitive recursive functions      3
Priority argument      89 142ff 163
Projection function      2
Q (sub-theory of arithmetic)      177
Quantifier Characterization of Sets Below 0/      13
RECURSIVE      see “Partial recursive”
Recursive approximation      13
recursive functions      13
Recursively enumerable (r.e.)      12 212 “f-r.e.” “n-r.e.”)
Recursively enumerable (r.e.) complete r.e. set      12
Recursively enumerable (r.e.) in A (in a)      12
Recursively isomorphic sets      136
Recursively isomorphic sets, theories      136
Relativize      31 96
Representable, a function,in arithmetic,is      177 178
S-m-n theorem      4
Simultaneously r.e. (s.r.e.)      172
Special on the Odds (S-O)      35
Special on the Odds (S-O), defining pair with respect to tree T      38
Special on the Odds (S-O), node      42
Special on the Odds (S-O), tree      38
Special, $\mathbb{M}$-      67 (see also “S-E” “S-X”)
Spector’s Theorem      23
Splitting, e-      17
Splitting, e-, at stages      17
Splitting, e-, tree      18
Splitting, tree      18
String(s), compatible      5
String(s), empty      5
String(s), extends      16
String(s), incompatible      5
String(s), length of      5
String(s), lies above, below      16
String(s), ordering of      6
Sublattice      187
Subtree      17
Successor function      2
T-predicate      3
Titgemeyer’s representation      226
Topped      74
Tower, $\underline{a}$-      133
TREE      15
Tree, $\mathbb{M}$-special      67
Tree, branching of      16
Tree, defining pair for level of      37
Tree, degree of      15
Tree, full subtree of      17
Tree, full-      17
Tree, fully uniform      37
Tree, identity      15
Tree, node of      16
Tree, of trees      96 220
Tree, partial recursive      17
Tree, S-O      38
Tree, S-X      54
Tree, splitting tree for e      18
Tree, subtree      17
Tree, uniform      37
Turing degree      9
Turing reducibility      9
Uniform tree      37
Upper-semi-lattice      187
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