Note on Representing $\aleph_0$-categorical Linear Orders

TL;DR

This paper presents a canonical normal form for representing countably infinite categorical linear orders, simplifying their classification based on Rosenstein's description.

Contribution

It introduces a unique minimal normal form for $oldsymbol{eth}_0$-categorical linear orders, enhancing their structural understanding.

Findings

Established a canonical normal form for these orders.

Provided a unique minimal representation.

Simplified classification of $oldsymbol{eth}_0$-categorical linear orders.

Abstract

These notes find a canonical representation of the $\aleph_0$-categorical linear orders based on Joseph Rosenstein's description. A unique minimal representation, called the normal form, is obtained.