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POINTCLASS

Pointclass

Descriptive set theory concept

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

Pointclass

Adequate pointclass

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

Adequate pointclass

Adequate_pointclass

Wadge hierarchy

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

Wadge hierarchy

Wadge_hierarchy

Scale (descriptive set theory)

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

Scale (descriptive set theory)

Scale_(descriptive_set_theory)

Inductive set

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

Inductive set

Inductive_set

Prewellordering

Set theory concept

If Γ {\displaystyle {\boldsymbol {\Gamma }}} is an adequate pointclass whose dual pointclass has the prewellordering property, then Γ {\displaystyle {\boldsymbol

Prewellordering

Determinacy

Subfield of set theory

(perfect-information game) determinacy for a boldface pointclass implies Blackwell determinacy for the pointclass. This, combined with the Borel determinacy theorem

Determinacy

Uniformization (set theory)

make the axiom of uniformization equivalent to the axiom of choice. A pointclass Γ {\displaystyle {\boldsymbol {\Gamma }}} is said to have the uniformization

Uniformization (set theory)

Uniformization_(set_theory)

Point class

Topics referred to by the same term

Point class may refer to Pointclass sets in mathematics Point-class sealift ship Point-class cutter This disambiguation page lists articles associated

Point class

Point_class

Difference hierarchy

difference hierarchy over a pointclass is a hierarchy of larger pointclasses generated by taking differences of sets. If Γ is a pointclass, then the set of differences

Difference hierarchy

Difference_hierarchy

Descriptive set theory

Subfield of mathematical logic

theory such as Kripke–Platek set theory and second-order arithmetic. Pointclass Prewellordering Scale property Kechris, Alexander S. (1994). Classical

Descriptive set theory

Descriptive_set_theory

Moschovakis coding lemma

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

Moschovakis coding lemma

Moschovakis_coding_lemma

Property of Baire

Difference of an open set by a meager set

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

Property of Baire

Property_of_Baire