Index
In the main items, Greek letters and mathematical symbols are alphabetized phoneti-
cally,disregardinghyphens,readingsuperscriptsbeforesubscripts,and(wherethefont
matters)givingprioritytolightfaceratherthanboldface: thusΣ2
1
isread sigmaonetwo,
it comes after Σn,
1
which is read sigmaonen and just before Σ2.
1
This convention is not
observedwithin eachitem, wheresub-andsubsub-itemsareordered“logically”, most
often following the order in which the terms occur in the text.
A , A
κ,52
closure of the Lusin pointclasses under A ,
2B.5, 56
closure of ¬Γ under A a Spector point-
class), 4C.6, 161
A-sets, same as analytic sets,
Σ1
1
absolutely Γ-inductive pointset, 312
absolutely measurable
function, 84
pointset, 83
- from determinacy hypotheses, 6A.18, 229
- for
Σ1
2
if κ (ℵ1), 6G.12, 289
- for Σ2
1
if (∀α)[card(N L(α)) = ℵ0],
8G.9, 425
absoluteness
basic theory, 8E
of a notion, for a collection of classes, 391
ZF-absoluteness, 392
of a function as an operation, 399
of a set as a condition, 399
of Σ1
2
pointsets as conditions, 8F.9, 409
AC, Axiom of Choice, 374
when it is needed, 7F
in L, 8F.3, 403
AD, Axiom of (full) Determinacy, 292basic the-
ory: 7D
AD, Axiom of (full) Determinacy, 292
adequate pointclass, 119
ℵ1 is measurable, under AD, 7D.18, 338
Alg(M,J) (algebraic points over M,relative to
J), 423
α#,
see remarkable character
|α| (ordinal coded by α), 147
α(n) = α(0),...,α(n 1) , 115
(α)i,31
α0,...,αk−1 , 31
ambiguous Borel pointclasses, see ∆n, 0 ∆0
analysis (the structure of), 356
analytic sets, same as
Σ1
1
analytical pointsets, 118
of type 0,1, formally definable, 8B.3, 367,
8B.12, 369
see also Kleene pointclasses
Approximation Theorem, 2H.1, 80
over standard models of ZF, 8G.8, 423
arithmetic (structure of), 355
arithmetic subtraction k
·
n,92
arithmetical pointsets, 118
properly included in
∆1,
1
3F.8, 130
formally defined, 8B.2, 367, 8B.11, 368
see also Kleene pointclasses
A(u) (subgame of A at u), 219
Axiom
of Choice, AC, see AC
of Dependent Choices, DC, see DC
of Determinacy, AD, see AD
see also ZF,ZFC,ZFL
Baire Category Theorem, 2H.2, 82
Baire functions, 45
relation with Borel functions, 1G.18, 45
1G.21, 46
continuous on a comeager G , 2H.10, 84
see also functions
Baire measurable functions, same as Baire func-
tions
Baire property, see property of Baire
Baire space, N,9
homeomorphic with the irrational numbers,
9
◦continuouslysurjectedontoeveryPolishspace,
1A.1, 10, 1G.2, 38
Borel isomorphic with every perfect product
space, 1G.4, 41
recursively presented, 97
◦recursivelysurjectedontoeveryproductspace,
3D.14, 116, 3E.6, 121

∆1-isomorphic
1
with every perfect product
space, 3E.7, 122
Baire-de la Vallee-Poussin class , 47
Banach-Mazur game
G∗∗(A),
X
226
basic theory: 6A.13, 226 6A.16, 227
bar (backwards) induction and recursion, 62
basic nbhds (center, radius), 11
recursively presented, 98
absolutely presented, 401
basic space, 14
basis, 179

∆1
1
not a basis for
Π0,
1
4D.10, 170

forΣ1
2
(Novikov-Kondo-Addison), 4E.5, 179
491
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