University Seminar: Logic Across Disciplines-Classification and measure for algebraic fields

Title:   Classification and measure for algebraic fields

Speaker:    Russell Miller, City University of New York

Date and Time: Friday, November 10, 2017, 03:00pm-04:00pm

Place: Rome Hall 771

Abstract:  The algebraic fields of characteristic 0 are precisely the subfields of the algebraic closure of the rationals, up to isomorphism.  We describe a way to classify them effectively, via a computable homeomorphism onto Cantor space.  This homeomorphism makes it natural to transfer Lebesgue measure from Cantor space onto the class of these fields, although there is another probability measure on the same class, which seems in some ways more natural than Lebesgue measure.  We will discuss how certain properties of these fields – notably, relative computable categoricity – interact with these measures:  the basic result is that only measure-0-many of these fields fail to be relatively computably categorical.  (The work on computable categoricity is joint with Johanna Franklin.)