Ahlbrandt and Ziegler show that the bi-interpretability class of a countably categorical theory is characterised by a topological group,
while for arbitrary theories Ben Yaacov has shown we can use topological groupoids.
These results can be expressed in the language of topos theory by equating the bi-interpretability class of a theory with its "classifying topos".
In this talk, we introduce the notion of elimination of parameters and use it to give a classification of which topological groupoids can represent
the classifying topos of a given theory. | 
