arXiv subjects
Publications and source records attributed to Mariana Vicaría.
We classify the imaginaries in a large class of equicharacteristic zero henselian valued fields that contain all those with bounded inertia group, and more. To do so, we consider a mix of sorts introduced in earlier works of the two authors and prove elimination of imaginaries down to the field, the k-linear imaginaries and the imaginaries of the value group.
We present a unifying framework of residual domination for (expansions of) henselian valued fields of equicharacteristic zero, encompassing some valued fields with operators. We show that the class of residually dominated types coincides with the types that are orthogonal to the value group, and with the class of types whose reduct to ACVF (the theory of algebraically closed valued fields with a non-trivial valuation) are generically stable. When the residue field is stable (resp. simple) we relate these equivalent notions to generic stability (resp. simplicity). Those results apply in particular to ultraproducts of $p$-adic fields and to the limit theory VFA$_{0}$ of algebraically closed valued fields of characteristic $p$ with the Frobenius automorphism (as $p$ tends to infinity).
This paper is devoted to understand groups definable in Presburger arithmetic. We prove the following theorems: Theorem 1. Every group definable in a model of Presburger Arithmetic is abelian-by-finite. Theorem 2. Every bounded group definable in a model (Z,+,<) of Presburger Arithmetic is definably isomorphic to (Z, +)^{n} mod out by a lattice.