Sunday, November 6, 20162:50 pmNERDS: New England Recursion & Definability SeminarScience Center, Room E104‚Äč, Wellesley College, Wellesley, MA

Comparing notions of effective genericity

Rose Weisshaar

Notre Dame University

Rose Weisshaar

In recent work, Cholak, Dzhafarov, Hirst and Slaman showed that for n ≥ 3, every Mathias n-generic computes a Cohen n-generic. It is natural to wonder how other types of generic objects compare to one another. We consider generics for an effective version of Hechler forcing. Adapting a method developed by Cholak, Dzhafarov, and Soskova, we show that for n ≥ 3, every Mathias n-generic computes a Hechler n-generic, and every Hechler n-generic computes a Mathias n-generic. Finally, we explore the (open) question of whether, for n ≥ 3, the Mathias n-generics and the Hechler n-generics occupy exactly the same Turing degrees.

Rose Weisshaar is a doctoral student at Notre Dame University, under the supervision of Peter Cholak.