## $$C$$-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

### Keywords:

quasiminimal set; C-quasiminimal set; enumeration degree
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