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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...

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...

property is related to the stronger scale property; in practice, many pointclasses having the prewellordering property also have the scale property, which...

scale property is a strengthening of the prewellordering property. For pointclasses of a certain form, it implies that relations in the given pointclass...