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. 
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     author = {N. A. Baklanova},
     title = {Minimal {Elements} and {Minimal} {Covers} in {Rogers} {Semilattice} of {Computable} {Numberings} in {Hyperarithmetical} {Hierarchy}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {77--84},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2011_11_3_a4/}
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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/