Extending the Ginsburg-Spanier Theorem to Functions and Mixed Arithmetic

Alain Finkel, Jérôme Leroux

We study sets and functions definable in the three additive theories $\FO(\Z,+,\leq)$, $\FO(\R,+,\leq)$, and $\FO(\R,\Z,+,\leq)$. The Ginsburg--Spanier theorem~\cite{GS66} characte…