March 1
Iian Smythe,
Rutgers University
Equivalence of generic reals
Given a countable transitive model of set theory and a notion of forcing in it, there is a natural countable Borel equivalence relation on generic objects over the model; two generics are equivalent if they yield the same generic extension. We study generic reals arising from familiar notions of forcing, e.g., Cohen and random forcing, under this equivalence relation and describe their relative complexity using the techniques of invariant descriptive set theory.