The elementary theory of the natural lattice is finitely axiomatizable
The author investigates the first order theory of the structure (\({\mathcal N}^*,|)\), where \({\mathcal N}^*\) is the set of positive integers and \(|\) is the divisibility relation. It is known that this theory, called DIV is consistent, complete, decidable and not categorical. In this paper it is shown that DIV is finitely axiomatizable. The author gives an explicit finite axiomatization of DIV and verifies the completeness of it by the method of elimination of quantifiers. In the proof some unpublished results obtained by the author in 1979 are used.
scientific article; zbMATH DE number 4154414