Journal of Symbolic Logic 80 (4):1182-1210 (2015)

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.
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DOI 10.1017/jsl.2015.3
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Some Orbits for E.Peter Cholak, Rod Downey & Eberhard Herrmann - 2001 - Annals of Pure and Applied Logic 107 (1-3):193-226.

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