Lattice initial segments of the Turing degrees
arXiv:0901.3876
Abstract
We characterize the isomorphism types of principal ideals of the Turing degrees below 0' that are lattices as the lattices with a Sigma-0-3 presentation, by showing that each Sigma-0-3 presentable bounded upper semilattice is isomorphic to such a principal ideal. We get a similar result for the Turing degrees below any degree above 0".
Doctoral dissertation, Logic and the Methodology of Science, University of California, Berkeley, 2002