Remarks, du côté de chez Tarski, on symmetric ternary relations

We point out that the results in 12] are the model-theoretic counterpart of results established syntactically in 3] and 10], and that Martin’s theorem for the Euclidean 3- or higher-dimensional case, established in 5], does not depend on the Beckman-Quarles theorem, and can be rephrased as a result about axiomatizability and definability.