Geodesic
Dual Covers of the~Greatest Element of the~Rogers Semilattice
Matematičeskie trudy, Tome 7 (2004) no. 2, pp. 98-108

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In the article, we study the algebraic structure of the Rogers semilattices of $\Sigma_n^0$-computable numberings for $n\ge2$. We prove that, under some sufficient conditions, the greatest element of each of these semilattices can be a limit element (i. e., cannot have dual covers). 
@article{MT_2004_7_2_a3,
     author = {S. Yu. Podzorov},
     title = {Dual {Covers} of {the~Greatest} {Element} of {the~Rogers} {Semilattice}},
     journal = {Matemati\v{c}eskie trudy},
     pages = {98--108},
     publisher = {mathdoc},
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     number = {2},
     year = {2004},
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     url = {http://geodesic.mathdoc.fr/item/MT_2004_7_2_a3/}
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S. Yu. Podzorov. Dual Covers of the~Greatest Element of the~Rogers Semilattice. Matematičeskie trudy, Tome 7 (2004) no. 2, pp. 98-108. http://geodesic.mathdoc.fr/item/MT_2004_7_2_a3/