Ivanova contact join-semilattices are not finitely axiomatizable
arXiv:2311.12599 · doi:10.1093/jigpal/jzaf008
Abstract
We show that the class of Contact join-semilattices, as introduced by T. Ivanova, is not finitely axiomatizable. On the other hand, a simple finite axiomatization exists for the class of those join semilattices with a weak contact relation which can be embedded into the reduct of a Boolean algebra (equivalently, a distributive lattice) with a weak contact relation.
v2 added a few details; some theorems are proved also for a pre-contact relation (i.e., symmetry not assumed)