-correct 217
-recursive 234
-recursively enumerable 236 241
-sets 22
-cardinal 158
-Finite 155
-finite injury 175
-jump 199
-recursive 155
-Recursive in 162
-recursively enumerable 154
-recursion 227
-sets 133
sets 18
2cf() 181
boundedness 20
Skolem function 160
Addison equivalence 48
Admissible ordinals 154 174
Admissible sets 151
Analytical in Y 42
Analytical predicates 3
Baire category 97 108
Basis theorems 52 74 92 250
Boldface 42
Boundedness, 20
Bounding arguments 81
Category 97
Ccc forcing 273
Choice, 67
Closure condition 7
Closure ordinals 76
Cofinality, 181
Cohen forcing 94
Comprehension, 67
Constructibility 82
Constructive in 43
Constructive ordinals 10
Converges 234
Countable chain selection 277
Countably closed forcing 265
Davis uniqueness 42
Density for 212
Divergence-admissibility split 257
Dynamic methods 184
Effective bounding 263
Effective transfinite recursion 10 238
Fine structure 207
First order definable 154
Forcing 94 98 265 273
Forcing computations 259
Full ordinal rank 64
Function quantifiers 4
Gandy forcing 108
Gandy selection 244
Gandy topology 108
Genericity 95 101 104
Grilliot selection 284
Harrington’s plus-two theorem 299
HYP 23
Hyperarithmetic 23
Hyperarithmetic predicates of reals 44
Hyperarithmetic quantifiers 59
Hyperarithmetic reducibility 44
Hyperdegrees, incomparable 46
Hyperdegrees, minimal 106
Hyperjump 48
Hyperregular 135 167
Incomparable hyperdegrees 46
Inductive definitions 76
Kechris’s basis theorem 250
Kleene’s 8
Kreisel compactness 70
Louveau separation 107
MacQueen — Harrington selection 284
Maximal Sets 145
Measureability of 47
Metacomplete 133
Metacomputable 123
| Metafinite 117
Metafinite computations 121
Metarecursive 117
Metarecursive in 127
Metarecursively enumerable 117
Minimal hyperdegrees 106
Monotonic 76
Moschovakis selection 287
Moschovakis witnesses 249
Mostowski’s conjecture 59
Natural enumeration of ) 155
Natural enumeration of 9
Negative requirements 221
Non-enumerability 266
Normal forms 5
Normann schemes 233
Normann selection 279
Notations for ordinals 8
Objects of type a 291
Ordinal analysis of sets 18
Ordinal rank 63
Partial -recursive 234
Partial recursive functions 3
Perfect forcing 98
Perfect subsets 71 84
persistent 26
Plus-one theorems 290
Positive 77
Positive requirements 220
Post’s problem for -recursion 328
Post’s problem for 177 182
Post’s problem for admissible sets 189
Post’s problem, uniform solution 191
Priority arguments 138 169 219 338
Projectum, -recursively enumerable 313
Projectum, 157
Projectum, 208
Projectum, tame 320
Ramified analytic hierarchy 62
RE cofinality 318
Recursive enumerability on 256
Recursive ordinals 15 241
Reduction 35
Reflection 242
Regular sets 129 131 163 165 309
Rogers and ETR 11
Scattered 86
Sections 291
Selection 32 283 304
Separation 36
Separation, Louveau 107
seq 18
sequence numbers 18
Set quantifiers 6
Shore blocking 186
Shore’s density theorem 218
Shore’s splitting theorem 204
Silver’s Theorem 112
SIMPLE 134
Simpson’s dichotomy 146
Singletons, 37 41
Singletons, 81 86
Slaman’s density theorem 337
Slaman’s splitting theorem 334
Spector — Gandy Theorem 61
Stability 159
Tame cofinality 323
Tame projectum 180
Tame recursion 194
Tameness 179
Tree of possibilities 261
Turing jump 22
Turing jump hierarchy 60
Uniformity, measure-theoretic 88
Uniformization 28 87
Unique notations 55
Uniqueness theorem, Spector’s 40
Universal computation tree 237
Weak admissibility 211 228
Wellfounded relations 16
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