On the theories classified by an étendue
arXiv:2507.04526 · doi:10.1112/blms.70430
Abstract
We give a model-theoretic characterisation of the geometric theories classified by étendues -- the `locally localic' topoi. They are the theories where each model is determined, syntactically and semantically, by any witness of a fixed collection of formulae.
Substantial changes, fixing an error in the previous version. 19 pages