Atomless \(r\)-maximal sets
type: Item
instance of: scholarly article
title: Atomless \(r\)-maximal sets
zbMATH Open document ID: 0936.03039
DOI: 10.1007/BF02780182
author: André Nies
author: Peter A. Cholak
published in: Israel Journal of Mathematics
publication date: 2000-02-14T00:00:00Z
review text: Let \(A\) be a computably enumerable set, and \(L(A)\) be the lattice of its supersets under the inclusion relation. It was proved earlier that for many sets \(A\), the filters \(L(A)\) are isomorphic. For example, for all low \(A\), by a result of R. Soare, \(L(A)\) are isomorphic to the lattice of all computably enumerable degrees, and, therefore, are isomorphic to each other. The last can also be said about the lattices \(L(A)\) for maximal sets \(A\). The authors decide a longstanding problem and show that there exist infinitely many pairwise incomparable sets \(L(A)\).
reviewed by: Sh. T. Ishmukhametov
Mathematics Subject Classification ID: 03D25
zbMATH DE Number: 1389713
zbMATH Keywords: computably enumerable set
zbMATH Keywords: lattice of supersets
zbMATH Keywords: filters
zbMATH Keywords: pairwise incomparable
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1389713