Denis Hirschfeldt : Attractive and Dispersive Degrees

Posted by Matthew Harrison-Trainor , part of the Logic Seminar.

At

April 1, 2025, 2:30 p.m.

In

636 SEO

Abstract

The upper density of the symmetric difference between two sets of natural numbers gives a notion of distance that can be used to define a metric on the Turing degrees. By work of Monin, this metric is (0,1/2,1)-valued. A degree a is attractive if almost every degree is at distance 1/2 from a, and dispersive otherwise. I will discuss joint work with Jockusch and Schupp, as well as more recent work of Royer, on the distribution of attractive and dispersive degrees, and their connections with the interplay between effective randomness and genericity.