The logic seminar today will be given by David Webb. A title and abstract are below.
Title: On The Levin-V’yugin Degrees
Abstract: I will define and discuss the Levin-V’yugin degrees, a measure algebra defined on collections of reals closed under Turing equivalence. Roughly speaking, in this ordering collections A and B have that A<B if for any probabilistic algorithm, the probability that it produces an element of A that is not in B is 0. Time permitting, I will prove that the computable reals and the random reals each form an atom in this Boolean algebra, and discuss other degrees and their positions in the lattice.
The paper this talk is based on is here: https://arxiv.org/pdf/1907.07815.pdf