2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60884We derive author's discrete forms of the Beckman-Quarles theorem from the definability results of Raphael M. Robinson.enlarged version, LaTeX2eMetric Geometry51M05Discrete versions of the Beckman-Quarles theorem from the definability results of Raphael M. Robinsontext