johnstone p 204 :

"in the suggestive terminology of tierney, we say that the topology j _forces_ f to be an interpretation of l"

hmm, l here is just a "language", but they go on to consider the case of a theory t as well ...

f here is... ???something like... ??the generic model of a "stuff-level" theory, to which forcing conditions / axioms / coverings are being added ... ??or something??

??something about ... maybe the "l" bit involves shoe-horning "structure-level" in with "property-level" to some extent ... ??or something ...