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.