Analytic Sets and Regularity Properties

John Howe, University of Leeds. Part of the postgraduate logic seminar series.

Descriptive Set Theory is the branch of set theory that concerns itself with the structure of Polish spaces in general and the real line in particular. Regularity properties of sets of reals, such as Lebesgue measurability, state that a set is "well behaved" in a certain sense. I will outline the approach taken to describing such sets and show that sufficiently simple sets satisfy most of the classical notions of regularity, one of which has an application in a noted theorem of model theory (see Rosario Mennuni's talk on Tuesday).