D-MAXIMAL SETS

Soare [20] proved that the maximal sets for man orbit in epsilon. 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.