Solon, B. Ya. \(C\)-quasiminimal enumeration degrees. (Russian, English) Zbl 1029.03029 Sib. Mat. Zh. 44, No. 1, 211-223 (2003); translation in Sib. Math. J. 44, No. 1, 174-183 (2003). A set \(A\) is called \(C\)-quasiminimal if \(C<_eA\) and for each total function \(g\), \(g\leq_eA\) implies \(g\leq_eC\).The author proves a series of results on the existence of families of \(C\)-quasiminimal sets such as chains and antichains. In particular, he proves that if \(\mathbf{c}<\text\textbf{a}\) and \(\mathbf{a}\) is total, then each at most countable partially ordered set is embeddable into the set of all \(\mathbf{c}\)-quasiminimal \(e\)-degrees which are less than \(\mathbf{a}\). Reviewer: A.S.Morozov (Novosibirsk) MSC: 03D30 Other degrees and reducibilities in computability and recursion theory Keywords:quasiminimal set; C-quasiminimal set; enumeration degree PDF BibTeX XML Cite \textit{B. Ya. Solon}, Sib. Mat. Zh. 44, No. 1, 211--223 (2003; Zbl 1029.03029); translation in Sib. Math. J. 44, No. 1, 174--183 (2003) Full Text: EuDML EMIS OpenURL