We use a new version of the Definability Theoremof Beth in order to unify classical theorems of Yuri Matiyasevich and Jan Denef in one structural statement. We give similar forms for other important definability results from Arithmetic and Number Theory.
"An isomorphism between monoids of external embeddings: about definability in arithmetic." J. Symbolic Logic 67 (2) 598 - 620, June 2002. https://doi.org/10.2178/jsl/1190150100