Higher arithmetic on the ordinals

2025/08/18 by Ducourtial, Adrian
#03E10 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2508.13334

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.

Related

• Transfinite iteration functionals and ordinal arithmetic
• Ordinal Notation
• Arithmetic, Infinite Trees, and Second-order Subsystems: Notes and Observations
• Higher Classes of Ordinals induced by <₁
• Proofs that Modify Proofs