Abstract:
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).
Key words:numbering, reducibility of numberings, $\Sigma^0_n$-computable numbering, the Rogers semilattice, cover, complete numbering, weak reducibility.
Fulltext:
PDF file (1185 kB)