Well I've got the topos-theory tag, and explain that it's a question about classifying toposes, so that should take care of the meaning of "coherent". And by "unpacking" I explain as "sorting out which non-coherent formulae hold in the generic model". I think adding those tags might do the job.
(Coherent logic, btw, is the fragment of first order logic with \top, \bot, conjunction, disjunction, and existential quantification; usually handled with the machinery of LJ. It's pretty fun.)
