Author

Garrett Ervin

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Preprint Aug 2026

The Additive Arithmetic of Linear Orders

We present a systematic development of the arithmetic of the class of linear orders under the ordered sum $(LO, +)$ and prove a number of new results. Our approach is based on a Euclidean algorithm for pairs of linear orders that almost additively commute. Among our results: (i.) We generalize and give unified proofs o...

Garrett Ervin, Eric Paul · 0 citations