Ɗ-MAXIMAL SETS

Soare [20] proved that the maximal sets form an orbit in ε. We consider here Ɗ-maximal sets, generalizations of maximal sets introduced by Herrmann and Kummer [12]. Some orbits of Ɗ-maximal sets are well understood, e.g., hemimaximal sets [8], but many are not. The goal of this paper is to define ne...

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Bibliographic Details
Published in:The Journal of symbolic logic 2015-12, Vol.80 (4), p.1182-1210
Main Authors: CHOLAK, PETER A., GERDES, PETER, LANGE, KAREN
Format: Article
Language:English
Subjects:
Automorphisms
Boolean algebras
Construction engineering
Flavors
Logical theorems
Mathematical lattices
Mathematical logic
Mathematical theorems
Recursively enumerable sets
Skeleton
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Summary:Soare [20] proved that the maximal sets form an orbit in ε. We consider here Ɗ-maximal sets, generalizations of maximal sets introduced by Herrmann and Kummer [12]. Some orbits of Ɗ-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 Ɗ-maximal sets. Although these invariants help us to better understand the Ɗ-maximal sets, we use them to show that several classes of Ɗ-maximal sets break into infinitely many orbits.
ISSN:0022-4812
1943-5886
DOI:10.1017/jsl.2015.3