${\aleph }_0$-categoricity of semigroups II

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.