We show that for any -r.e. degree and -r.e. degree with , there is an -r.e. degree strictly between and . We also show that there is a maximal incomplete -r.e. degree. As a corollary, is not a -elementary substructure of .
"Weak Density and Nondensity among Transfinite Levels of the Ershov Hierarchy." Notre Dame J. Formal Logic 61 (4) 521 - 536, November 2020. https://doi.org/10.1215/00294527-2020-0023