English

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.

Keywords

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

R2 v1 2026-07-01T04:55:37.606Z