Title: Fickleness and bounding lattices in the recursively enumerable Turing degrees
by Li Ling Ko (University of Notre Dame) as part of Computability theory and applications

Abstract
The ability for a recursively enumerable Turing degree $d$ to bound certain
important lattices depends on the degree’s fickleness. For instance, $d$
bounds $L_7$ (1-3-1) if and only if $d$’s fickleness is $>omega$
($geqomega^omega$). We work towards finding a lattice that characterizes
the $>omega^2$ levels of fickleness and seek to understand the challenges
faced in finding such a lattice. The candidate lattices considered include
those that are generated from three independent points, and upper
semilattices that are obtained by removing the meets from important
lattices.