Rogers semilattices of families of two embedded sets in the Ershov hierarchy
This paper examines computable numberings, specifically the Rogers semilattices induced by families of sets at different levels of the Ershov hierarchy -- see [\textit{S. A. Badaev} and \textit{Zh. T. Talasbaeva}, in: Mathematical logic in Asia. Proceedings of the 9th Asian logic conference, Novosibirsk, Russia, 2005. Hackensack, NJ: World Scientific. 17--30 (2006; Zbl 1123.03042)]. The authors focus on the possible cardinality of such a semilattice, in particular, conditions under which the semilattice is infinite and conditions under which it is a singleton.
scientific article; zbMATH DE number 6081356