Finitely generated codings and the degrees r.e. in a degree 𝑑

Shore, Richard A.

doi:10.1090/S0002-9939-1982-0637179-1

Finitely generated codings and the degrees r.e. in a degree $\textbf {d}$
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Proc. Amer. Math. Soc. 84 (1982), 256-263 Request permission

Abstract:

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

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