Diophantine sets. Preliminaries

Abstract

Summary In this article, we define Diophantine sets using the Mizar formalism. We focus on selected properties of multivariate polynomials, i.e., functions of several variables to show finally that the class of Diophantine sets is closed with respect to the operations of union and intersection. This article is the next in a series [1], [5] aiming to formalize the proof of Matiyasevich’s negative solution of Hilbert’s tenth problem.