A countable meet of spatial sublocales of a coherent space is spatial

**Abstract:**

This represents joint work with J. Kennison and R. Raphael

This will consist of two talks. The first will be an exposition of
known properties of coherent spaces, locales, and sublocales,
including the 1-1 correspondence between equivalence relations
on a frame and nuclei. The second talk will be devoted to showing
first that if X is the space of equivalence relations on the models of
a theory described by a set of finitary partial
operations, equipped with the Zariski topology, then X is coherent.
The second thing I will prove is the theorem of the title.