| Résume | Elimination of imaginaries is a fundamental structural property in model theory, which roughly means that definable equivalence classes can be coded by tuples of elements from the structure, allowing us to treat them as ordinary elements of the structure. In the context of valued fields, significant progress was initiated by Haskell, Hrushovski, and Macpherson, who described a language in which the theory ACVF eliminates imaginaries. Building on this foundation, Rideau-Kikuchi and Montenegro proved elimination of imaginaries for bounded pseudo p-adically closed fields equipped with finitely many independent valuations. In this talk, I will explain how their techniques can be adapted to prove weak elimination of imaginaries for perfect bounded PAC fields equipped with finitely many independent valuations. The strategy combines an extension theorem for types to invariant types with an amalgamation result. |
