# Blog Archives

# Topic Archive: effective genericity

NERDS: New England Recursion & Definability SeminarSunday, November 6, 20162:50 pmScience Center, Room E104, Wellesley College, Wellesley, MA

# Comparing notions of effective genericity

Notre Dame University

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.