<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p><p>This article is the next in a series [<xref ref-type="bibr" rid="j_forma-2018-0007_ref_001_w2aab3b7b6b1b6b1ab1ab1Aa">1</xref>], [<xref ref-type="bibr" rid="j_forma-2018-0007_ref_005_w2aab3b7b6b1b6b1ab1ab5Aa">5</xref>] aiming to formalize the proof of Matiyasevich’s negative solution of Hilbert’s tenth problem.</p></abstract>

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.

Diophantine sets. Preliminaries

Formalized Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Diophantine sets. Preliminaries"}

In this article, we define Diophantine sets using the Mizar formalism. We focus on selected properties of multivariate polynomials, i.e., functions of several...

Diophantine sets. Preliminaries

Publié en ligne: 28 juil. 2018

Pages: 81 - 90

Reçu: 27 mars 2018

DOI: https://doi.org/10.2478/forma-2018-0007

Mots clés
Hilbert’s 10th problem, Pell’s equation, multivariate polynomials

© 2018 Karol Pąk, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Diophantine sets. Preliminaries

Publié en ligne: 28 juil. 2018

Pages: 81 - 90

Reçu: 27 mars 2018

DOI: https://doi.org/10.2478/forma-2018-0007

Mots clésHilbert’s 10th problem, Pell’s equation, multivariate polynomials

© 2018 Karol Pąk, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
Hilbert’s 10th problem, Pell’s equation, multivariate polynomials