On the first-order theory of the remainder
Logic
2025-06-05 v1
Abstract
It is proved that the first-order theory of the structure (N,mod) is undecidable. Here mod denotes the operation of computing the remainder for any division between positive integers; i.e. x mod y is the remainder obtained by the division x : y.
Cite
@article{arxiv.2506.03204,
title = {On the first-order theory of the remainder},
author = {Mihai Prunescu},
journal= {arXiv preprint arXiv:2506.03204},
year = {2025}
}
Comments
2 pages