Olivia Caramello

Universal models and definability

We establish some general results on universal models in Topos Theory and show that the investigation of such models can shed light on problems of definability in Logic as well as on De Morgans law and the law of excluded middle for Grothendieck toposes.

Fraïssé’s Construction from a Topos-Theoretic Perspective

We present a topos-theoretic interpretation of (a categorical generalization of) Fraïssé’s construction in Model Theory, with applications to homogeneous models and countably categorical theories.

Atomic toposes and countable categoricity

We give a model-theoretic characterization of the class of geometric theories classified by an atomic topos having enough points; in particular, we show that every complete geometric theory classified by an atomic topos is countably categorical. Various results on atomic toposes are also established, and some applications are discussed.

Syntactic categories for Nori motives

We give a new construction, based on categorical logic, of Nori’s

A General Method for Building Reflections

\mathbb Q

Topologies for intermediate logics

Q-linear abelian category of mixed motives associated to a cohomology or homology functor with values in finite-dimensional vector spaces over

Lattices of theories

\mathbb Q