Diophantine undecidability for addition and divisibility in polynomial rings
Volume 182 / 2004
Fundamenta Mathematicae 182 (2004), 205-220
MSC: Primary 03B25, 12L05; Secondary 11U05.
DOI: 10.4064/fm182-3-2
Abstract
We prove that the positive-existential theory of addition and divisibility in a ring of polynomials in two variables $A[t_1,t_2 ]$ over an integral domain $A$ is undecidable and that the universal-existential theory of $A[t_1]$ is undecidable.
