A b s t r a c t. The notion of the first-order predicate logic determined by a relational system was introduced in Prucnal, T., Logics of relational systems, Bulletin of the Section of Logic, Polish Academy of Sciences, Vol.l9, nr 2 (1990), 58-60. In this paper we consider the pure first-order predicate logic determined by the system of natural numbers with identity. We show that this logic is axiomatizable.