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.

中文翻译：

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$$\aleph _0$$-半群的范畴 II

一个可数半群是 $\aleph_0$-categorical 如果它可以通过它的一阶性质来表征，直到同构。在本文中，我们继续研究半群的 $\aleph_0$-范畴。我们的主要结果是 $\aleph_0$-categorical 正统完全 0-simple 半群的完整分类，以及半群的某些类强半格的 $\aleph_0$-categorical 成员的描述。