Definition of Pointclasses. Meaning of Pointclasses. Synonyms of Pointclasses

- stated in terms of the determinacy of various pointclasses, which in turn implies that sets in those pointclasses (or sometimes larger ones) have regularity...
- more generally, subsets of Polish spaces. It begins with the study of pointclasses in the Borel hierarchy and extends to the study of more complex hierarchies...
- prove the determinacy of larger pointclasses, higher in the Wadge hierarchy, and the determinacy of such pointclasses, in turn, proves the existence of...
- Woodin (1999) as part of an attempt to generalize the theory of determinacy of pointclasses to cover the structure H ℵ 2 {\displaystyle H_{\aleph _{2}}} . Just as...
- the difference hierarchy over a pointclass is a hierarchy of larger pointclasses generated by taking differences of sets. If Γ is a pointclass, then the...
- property is related to the stronger scale property; in practice, many pointclasses having the prewellordering property also have the scale property, which...
- uniformization property is implied by the scale property, at least for adequate pointclasses of a certain form. It follows from ZFC alone that Π 1 1 {\displaystyle...
- scale property is a strengthening of the prewellordering property. For pointclasses of a certain form, it implies that relations in the given pointclass...