$\aleph_0$-categoricity of semigroups II

TL;DR

This paper advances the classification of countable semigroups that are uniquely characterized by their first-order properties, focusing on orthodox completely 0-simple semigroups and certain strong semilattices.

Contribution

It provides a complete classification of $eth_0$-categorical orthodox completely 0-simple semigroups and describes $eth_0$-categorical members of specific classes of strong semilattices.

Findings

Complete classification of $eth_0$-categorical orthodox completely 0-simple semigroups.

Descriptions of $eth_0$-categorical members in classes of strong semilattices.

Advancement in understanding the model-theoretic properties of semigroups.

Abstract

A countable semigroup is $\aleph_0$-categorical if it can be characterised, up to isomorphism, by its first-order properties. In this paper we continue our investigation into the $\aleph_0$-categoricity of semigroups. Our main results are a complete classification of $\aleph_0$-categorical orthodox completely 0-simple semigroups, and descriptions of the $\aleph_0$-categorical members of certain classes of strong semilattices of semigroups.