Date/Time Date(s) - 07/10/202412:30 pm - 1:30 pm
Location: HH 410
Title: Stable domination in a family of power series fields with analytic structure.
Speaker: Carlos Cardoba
Abstract: Studying the relationship between the types on a valued field structure with their restriction over distinct sorts of the language is a feature called domination. Ealy, Haskell and Ma?’iková showed that types over an o-minimal expansion of a real closed valued field are dominated by the value group and the residue field.
In this talk, I will present ongoing work under the supervision of Deirdre Haskell, towards a possible generalization of the domination statement to o-minimal expansions of real closed valued fields with an analytic structure. In particular, we followed Mourgues’ approach to power series field extensions of the real numbers as a starting point to study possible interpretations of restricted analytic functions in an extended model. Finally, we will present that under the previous construction similar domination results are obtained for a family of power series fields extending the real numbers.