Recursively enumerable sets of polynomials over a finite field are Diophantine期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Recursively enumerable sets of polynomials over a finite field are Diophantine

Authors:	Jeroen Demeyer

Institution:	(1) Department of Pure Mathematics and Computer Algebra, Ghent University, Galglaan 2, 9000 Gent, Belgium

Abstract:	We construct a Diophantine interpretation of $\mathbb{F}_qW,Z]$ over $\mathbb{F}_qZ]$ . Using this together with a previous result that every recursively enumerable (r.e.) relation over $\mathbb{F}_qZ]$ is Diophantine over $\mathbb{F}_qW,Z]$ , we will prove that every r.e. relation over $\mathbb{F}_qZ]$ is Diophantine over $\mathbb{F}_qZ]$ . We will also look at recursive infinite base fields $\mathbb{F}$ , algebraic over $\mathbb{F}_p$ . It turns out that the Diophantine relations over $\mathbb{F}Z]$ are exactly the relations which are r.e. for every recursive presentation.

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