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- Maximal_set abstract "In recursion theory, the mathematical theory of computability, a maximal set is a coinfinite recursively enumerable subset A of the natural numbers such that for every further recursively enumerable subset B of the natural numbers, either B is cofinite or B is a finite variant of A or B is not a superset of A. This gives an easy definition within the lattice of the recursively enumerable sets.Maximal sets have many interesting properties: they are simple, hypersimple, hyperhypersimple and r-maximal; the latter property says that every recursive set R contains either only finitely many elements of the complement of A or almost all elements of the complement of A. There are r-maximal sets that are not maximal; some of them do even not have maximal supersets. Myhill (1956) asked whether maximal sets exist and Friedberg (1958) constructed one. Soare (1974) showed that the maximal sets form an orbit with respect to automorphism of the recursively enumerable sets under inclusion (modulo finite sets). On the one hand, every automorphism maps a maximal set A to another maximal set B; on the other hand, for every two maximal sets A, B there is an automorphism of the recursively enumerable sets such that A is mapped to B.".
- Maximal_set wikiPageID "10495079".
- Maximal_set wikiPageLength "2662".
- Maximal_set wikiPageOutDegree "13".
- Maximal_set wikiPageRevisionID "638561052".
- Maximal_set wikiPageWikiLink Annals_of_Mathematics.
- Maximal_set wikiPageWikiLink Automorphism.
- Maximal_set wikiPageWikiLink Category:Computability_theory.
- Maximal_set wikiPageWikiLink Cofiniteness.
- Maximal_set wikiPageWikiLink Computability_theory.
- Maximal_set wikiPageWikiLink Hyperhypersimple.
- Maximal_set wikiPageWikiLink Lattice_(order).
- Maximal_set wikiPageWikiLink Mathematics.
- Maximal_set wikiPageWikiLink Modulo_(jargon).
- Maximal_set wikiPageWikiLink Natural_number.
- Maximal_set wikiPageWikiLink Recursively_enumerable_set.
- Maximal_set wikiPageWikiLink Simple_set.
- Maximal_set wikiPageWikiLinkText "Maximal set".
- Maximal_set wikiPageWikiLinkText "maximal set".
- Maximal_set wikiPageWikiLinkText "maximal".
- Maximal_set wikiPageUsesTemplate Template:Citation.
- Maximal_set wikiPageUsesTemplate Template:Mathlogic-stub.
- Maximal_set subject Category:Computability_theory.
- Maximal_set comment "In recursion theory, the mathematical theory of computability, a maximal set is a coinfinite recursively enumerable subset A of the natural numbers such that for every further recursively enumerable subset B of the natural numbers, either B is cofinite or B is a finite variant of A or B is not a superset of A.".
- Maximal_set label "Maximal set".
- Maximal_set sameAs Q6795644.
- Maximal_set sameAs m.02qftcg.
- Maximal_set sameAs Q6795644.
- Maximal_set wasDerivedFrom Maximal_set?oldid=638561052.
- Maximal_set isPrimaryTopicOf Maximal_set.