Non-Diophantine sets in rings of functions
Number Theory
2022-10-20 v1 Logic
Abstract
Except for a limited number of cases, a complete classification of the Diophantine sets of polynomial rings and fields of rational functions seems out of reach at present. We contribute to this problem by proving that several natural sets and relations over these structures are not Diophantine.
Keywords
Cite
@article{arxiv.2210.10556,
title = {Non-Diophantine sets in rings of functions},
author = {Natalia Garcia-Fritz and Hector Pasten and Thanases Pheidas},
journal= {arXiv preprint arXiv:2210.10556},
year = {2022}
}