- In the
mathematical field of
descriptive set theory, a
pointclass is a
collection of sets of points,
where a
point is
ordinarily understood to be an element...
- In the
mathematical field of
descriptive set theory, a
pointclass can be
called adequate if it
contains all
recursive pointsets and is
closed under recursive...
-
pointclass Γ, we want the
prewellorderings below a
given point in A to be
uniformly represented both as a set in Γ and as one in the dual
pointclass of...
-
pointclass. Equivalently, for each
ordinal α ≤ θ the
collection Wα of sets that show up
before stage α is a
pointclass. Conversely,
every pointclass is...
- (perfect-information game)
determinacy for a
boldface pointclass implies Blackwell determinacy for the
pointclass. This,
combined with the
Borel determinacy theorem...
- n,
together with a real parameter. The
inductive sets form a
boldface pointclass; that is, they are
closed under continuous preimages. In the
Wadge hierarchy...
- The
converse does not hold; however, if
every game in a
given adequate pointclass Γ {\displaystyle \Gamma } is determined, then
every set in Γ {\displaystyle...
- If Γ {\displaystyle {\boldsymbol {\Gamma }}} is an
adequate pointclass whose dual
pointclass has the
prewellordering property, then Γ {\displaystyle {\boldsymbol...
-
lemma may be
expressed generally as follows: Let Γ be a non-selfdual
pointclass closed under real
quantification and ∧, and ≺ a Γ-well-founded relation...
-
theory such as Kripke–Platek set
theory and second-order arithmetic.
Pointclass Prewellordering Scale property Kechris,
Alexander S. (1994). classical...
