We establish a criterion for deciding whether a class of structures is the class of models of a geometric theory inside Grothendieck toposes; then we specialize this result to obtain a characterization of the infinitary first-order theories which are geometric in terms of their models in Grothendieck toposes, solving a problem posed by Ieke Moerdijk in 1989. © 2010 Elsevier B.V.
Caramello, O. (2011). A characterization theorem for geometric logic. Annals of Pure and Applied Logic, 162(4), 318–321. https://doi.org/10.1016/j.apal.2010.08.004