Local initial segments of the Turing degrees
Bjørn Kjos-Hanssen, Bjørn Kjos-Hanssen, Theodore A. Slaman, Theodore A. Slaman · 2002
Abstract. Recent results on initial segments of the Turing degrees are presented, and some conjectures about initial segments that have implications for the existence of nontrivial automorphisms of the Turing degrees are indicated. §1. Introduction. This article concerns the algebraic study of the upper semilattice of Turing degrees. Upper semilattices of interest in this regard tend to have a least element, hence for convenience the following definition is made. Definition 1.1. A unital semilattice (usl) is a structure L = (L, ∗, e) satisfying the following equalities for all a, b, c ∈ L.