D-MAXIMAL SETS. (22nd December 2015) - CHOLAK, PETER A.; GERDES, PETER; LANGE, KAREN
Abstract: Soare [20] proved that the maximal sets form an orbit in E . We consider here D -maximal sets, generalizations of maximal sets introduced by Herrmann and Kummer [12]. Some orbits of 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 D -maximal sets. Although these invariants help us to better understand the D -maximal sets, we use them to show that several classes of D -maximal sets break into infinitely many orbits.