2016 seminar talk: Descriptive Set Theory and Absoluteness

Talk held by Sy-David Friedman (KGRC) at the KGRC seminar on 2016-03-10.


One of the initial motivations for the development of descriptive set theory (Borel-Baire-Lebesgue in Paris, Lusin-Egorov in Moscow) was to avoid the difficuilties of abstract set theory by focusing on sets of reals which have definitions of low complexity. In this talk I'll take a look at the extent to which this idea succeeds in the study of definable equivalence relations. An analytic equivalence relation can have countably-many (small), uncountably-many but not perfectly-many (medium), or perfectly-many classes (large); in the last case it can be either Borel or non-Borel.

The classes of an analytic equivalence relation can be countable (small) or contain a perfect set (large). For co-analytic equivalence relations they can also be uncountable with no perfect subset (medium). In either case a large class can either be Borel or non-Borel. I'll discuss the absoluteness/non-absoluteness of these notions as well as some related questions which connect to issues in the theory of class forcing.

Bottom menu

Kurt Gödel Research Center for Mathematical Logic. Währinger Straße 25, 1090 Wien, Austria. Phone +43-1-4277-50501. Last updated: 2010-12-16, 04:37.