Higher arithmetic on the ordinals
Logic
2025-08-26 v2
Abstract
We motivate and study an infinite sequence of binary operations on the ordinal numbers, extending the standard arithmetic on the ordinals to higher degrees of iteration. Connections to the hyperoperations on the natural numbers are discussed.
Cite
@article{arxiv.2508.13334,
title = {Higher arithmetic on the ordinals},
author = {Adrian Ducourtial},
journal= {arXiv preprint arXiv:2508.13334},
year = {2025}
}
Comments
11 pages. Added proof of monotonicity