Borisov Axioms Admit Persistent Euclidean Models Over Non-Archimedean Ordered Fields

The work converts Borisov's background assumptions into explicit axioms and drops the implicit real-number requirement on quantities. Over non-Archimedean fields the authors explicitly build Euclidean isometry models that satisfy the relativity principle yet cannot be eliminated by adding time's arrow or forbidding instantaneous motion, unlike the Archimedean case. This produces an infinite descending chain of distinct worldview-transformation groups in each geometry, a structure impossible over the reals. The result shows that the classical-relativistic dichotomy Borisov derived is field-dependent rather than logically forced. Related work by Andréka, Madarász and Németi on first-order axiomatizations of relativity (Studia Logica 2012) and by Székely on definability in spacetime theories supplies the logical toolkit used here. The chief limitation is the absence of any experimental or observational test; strengthening would require deriving a measurable signature unique to non-Archimedean models that could be sought in high-precision timing or cosmology data.