Imaginaries in separably closed valued fields

We show that separably closed valued fields of finite imperfection degree (either with lambda-functions or commuting Hasse derivations) eliminate imaginaries in the geometric language. We then use this classification of interpretable sets to study stably dominated types in those structures. We show that separably closed valued fields of finite imperfection degree are metastable and that the space of stably dominated types is strict pro-definable

Ind- and Pro- definable sets

We describe the ind- and pro- categories of the category of definable sets, in some first order theory, in terms of points in a sufficiently saturated model.Comment: 8 pages; Part of author's phd thesi

Higher internal covers

We define and study a higher-dimensional version of model theoretic internality, and relate it to higher-dimensional definable groupoids in the base theory.Comment: 32 pages, corrected version after comments from referee. To appear in "Model Theory