-MAXIMAL SETS
Peter A. Cholak, Peter Gerdes, Karen Lange · Journal of Symbolic Logic · 2015
Abstract Soare [20] proved that the maximal sets form an orbit in ${\cal E}$ . We consider here ${\cal D}$ -maximal sets, generalizations of maximal sets introduced by Herrmann and Kummer [12]. Some orbits of ${\cal D}$ -maximal sets are well understood, e.g., hemimaximal sets [8], but many are not. The goal of this paper is to define new invariants on computably enumerable sets and to use them to give a complete nontrivial classification of the ${\cal D}$ -maximal sets. Although these invariants help us to better understand the ${\cal D}$ -maximal sets, we use them to show that several classes of ${\cal D}$ -maximal sets break into infinitely many orbits.