pointclass

pointclass
A collection of sets of points (ordinarily understood to be elements of some perfect Polish space), characterized by some sort of definability property.

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  • Pointclass — 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 of some perfect Polish space. In practice, a pointclass is usually characterized by some… …   Wikipedia

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  • Difference hierarchy — In set theory, 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 set of differences in Γ is . In usual notation, this set is denoted by 2 Γ.… …   Wikipedia

  • Descriptive set theory — In mathematical logic, descriptive set theory is the study of certain classes of well behaved subsets of the real line and other Polish spaces. As well as being one of the primary areas of research in set theory, it has applications to other… …   Wikipedia

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