Logic Seminar

Russell MillerQueens College and CUNY Graduate Center
Classification and measure for algebraic fields

Wednesday, August 23, 2017 - 4:00pm
Malott 206

The algebraic fields of characteristic 0 are precisely the subfields of the algebraic closure of the rationals, up to isomorphism. Continuing a topic introduced in this seminar last May, 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, but 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.