A higher arithmetic on the ordinals

Adrian Ducourtial

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arXiv · 2508.13334

A higher arithmetic on the ordinals

Adrian Ducourtial

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Abstract

We motivate and study an infinite sequence of binary operations on the ordinal numbers, providing a common extension of the standard arithmetic on the ordinals and the hyperoperations on the naturals.

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Adrian Ducourtial. 2025-08-18. A higher arithmetic on the ordinals. https://arxiv.org/abs/2508.13334

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