Geodesic
Lattice properties of Rogers semilattices of compuatble and generalized computable familie
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1927-1936

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We consider the distributivity property and the property of being a lattice of Rogers semilattices of generalized computable families. We prove that the Rogers semilattice of any nontrivial $A$-computable family is not a lattice for every non-computable set $A$. It is also proved that if a set $A$ is non-computable then the Rogers semilattice of any infinite $A$-computable family is not weakly distribuive. Furtermore, we find two infinite computable families with nontrivial distributive and properly weakly distributive nontrivial Rogers semilattices.
Keywords: computable enumeration, generalized computable enumeration, $A$-computable enumeration, Rogers semilattice. 
@article{SEMR_2019_16_a32,
     author = {M. Kh. Faizrahmanov},
     title = {Lattice properties of {Rogers} semilattices of compuatble and generalized computable familie},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1927--1936},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a32/}
}
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M. Kh. Faizrahmanov. Lattice properties of Rogers semilattices of compuatble and generalized computable familie. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1927-1936. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a32/