**MW:** An addendum to the last post. I *do* have an employment opportunity for one of those pathological scaffolds: the one where *B*(0) is the 2-element boolean algebra, and all the *B*(*n*)’s with *n*>0 are trivial. It’s perfect for the semantics of a structure with an empty domain.

The empty structure has a vexed history in model theory. Traditionally, authors excluded it from the get-go, but more recently some have rescued it from the outer darkness. (Two data points: Hodges’ *A Shorter Model Theory* allows it, but Marker’s *Model Theory: An Introduction* forbids it.)