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\(C\)-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 \(\mathbf{a}\).

MSC:

03D30 Other degrees and reducibilities in computability and recursion theory
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