Descriptive set theory: Difference between revisions

Revision as of 04:35, 20 May 2010

Revision as of 04:35, 20 May 2010

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The area of [[effective descriptive set theory]] combines the methods of descriptive set theory with those of [[generalized recursion theory]] (especially [[hyperarithmetical theory]]). In particular, it focuses on [[lightface]] analogues of hierarchies of classical descriptive set theory. Thus the [[hyperarithmetic hierarchy]] is studied instead of the Borel hierarchy, and the [[analytical hierarchy]] instead of the projective hierarchy. This research is related to weaker version of set theory such as [[Kripke-Platek set theory]] and [[second-order arithmetic]].

== Applications ==

Much of descriptive set theory derives from ideas in [[topology]] and [[analysis]], and interactions between these fields continues. Recent work by [Alexander S. Kechris|[Kechris]] and [[Hjorth]] on applications of ideas from descriptive set theory to ergodic theory and the study of group actions and operator algebras has been especially influential.

==See also==