Geodesic
Minimal Elements and Minimal Covers in Rogers Semilattice of Computable Numberings in Hyperarithmetical Hierarchy
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 3, pp. 77-84

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Proved that Rogers semilattice of any infinite $\Sigma_{\omega}$-computable family contains infinitely many minimal elements, and each non-$0'$-universal numbering has infinitely many minimal covers.
Keywords: numbering, Rogers semilattice, hyperarithmetical hierarchy, minimal elements, minimal covers. 
N. A. Baklanova. Minimal Elements and Minimal Covers in Rogers Semilattice of Computable Numberings in Hyperarithmetical Hierarchy. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 3, pp. 77-84. http://geodesic.mathdoc.fr/item/VNGU_2011_11_3_a4/
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