It is commonly stated that while the author of Acts records some conversions that resulted from Paul's Athenian ministry, it is unlikely that a church was established in the city. This article argues, through an analysis of the use of the κολλάω word family in Luke-Acts, the Septuagint, early Christian writings and other relevant texts, that Luke uses the participle κολληθέντɛς as a way of signifying that a Christian community was indeed gathered together in Athens at this time. Leaving other social groups to join Paul and the other new believers, the new group is fused together by their shared faith, forming a new faith community in this ancient city.

We show that there is a cuppable c.e. degree, all of whose cupping partners are high. In particular, not all cuppable degrees are ${\operatorname {\mathrm {low}}}_3$-cuppable, or indeed ${\operatorname {\mathrm {low}}}_n$ cuppable for any n, refuting a conjecture by Li. On the other hand, we show that one cannot improve highness to superhighness. We also show that the ${\operatorname {\mathrm {low}}}_2$-cuppable degrees coincide with the array computable-cuppable degrees, giving a full understanding of the latter class.

We consider several familiar varieties of completely regular semigroups such as groups and completely simple semigroups. For each of them, we characterize their members in terms of absence of certain kinds of subsemigroups, as well as absence of certain divisors, and in terms of a homomorphism of a concrete semigroup into the semigroup itself. For each of these varieties $ \mathcal{V} $ we determine minimal non-$ \mathcal{V} $ varieties, provide a basis for their identities, determine their join and give a basis for its identities. Most of this is complete; one of the items missing is a basis for identities for minimal nonlocal orthogroups. Three tables and a figure illustrate the results obtained.