Finitely generated codings and the degrees r.e. in a degree ๐
Richard A. Shore ยท Proceedings of the American Mathematical Society ยท 1982
We introduce finitely generated (partial) lattices which can be used to code an arbitrary set D D . Results of Lerman, Shore and Soare are used to embed these lattices in the degrees r.e. in D D . Thus if the degrees r.e. in and above d {\mathbf {d}} are isomorphic to those r.e. in and above c {\mathbf {c}} , d {\mathbf {d}} and c {\mathbf {c}} are of the same arithmetic degree. Similar applications are given to generic degrees and general homogeneity questions.