2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119801We consider the fragment F of first order arithmetic in which quantification is restricted to ''for all but finitely many.'' We show that the integers form an F-elementary substructure of the real numbers. Consequently, the F-theory of arithmetic is decidable.LogicMathematical Physics03F30text