Logic Seminar

Ronnie Chen University of Illinois at Urbana--Champaign
Some results in descriptive locale theory

Friday, April 9, 2021 - 3:00pm

A locale is, informally, a topological space without an underlying set of points, with only an abstract lattice of "open sets". A recurring theme in locale theory is that omission of points removes many of the pathologies of point-set topology; instead, locale theory behaves like a generalization of "nice" topology, i.e., classical descriptive set theory, but without any countability restrictions. This talk will present some localic generalizations of well-known classical results: a boundedness theorem for analytic sets, and a Lusin--Novikov uniformization theorem. If time permits, I will also outline the theory of Baire category quantifiers for continuous open locale maps, and some of its applications to localic groups and their actions.