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. Equivalently, for each ordinal α ≤ θ the collection Wα of sets that show up before stage α is a pointclass. Conversely, every pointclass is...

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...

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

dictionary. Boldface may refer to: A variety of emphasis (typography) Boldface pointclass, a concept in descriptive set theory in mathematics Bold (disambiguation)...

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...

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...

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...

Kripke–Platek set theory and second-order arithmetic. This box: view talk edit Pointclass Prewellordering Scale property Kechris, Alexander S. (1994). Classical...

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

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...

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