A definitional view of Vogt's variant of the Mazur-Ulam theorem (Q2765371)

Generalizing a theorem of Mazur and Ulam, Vogt proved that equidistance-preserving transformations between real normed spaces of any dimension \(2,3,4,\dots\) are affine similarities. Further generalizations were prove by Skof. In this note the author reformulates these theorems as explicit definability results from implicit definitions in the logic \(L_{\omega_1\omega}\).NEWLINENEWLINEFor the entire collection see [Zbl 0972.00028].