Proceedings of a conference held at Centre de recherches mathematiques of the Universite de Montreal, June 18-20, 2009.

Includes bibliographical references and index.

The number of countable models in categories of sheaves ; Pseudomonodacity and 2-stack completions ; Purity and pure-injectivity for topological modules ; Model theory vs. categorical logic: Two approaches to pretopos completion (a.k.a. ^\mathrm eq ; The dialectica monad and its cousins ; A categorical approach to internality ; Computable structures of Scott rank omega _1^\mathrm CK ; The Lorentz category in special relativity ; A model-theoretic counterpart to Moishezon morphisms ; Generic stability, regularity, and quasiminimality ; Indexed Lawvere theories for local state ; Model theory in additive categories ; A derivation of Einstein's vacuum field equations ; An adventure into Hungarian word order with cyclic pregroups ; No limit model in inaccessibles ; The strict omega groupoid interpretation of type theory ; Lax monoidal fibrations