An approximate Ax-Kochen-Ershov principle for valued fields in continuous logic

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Abstract

In a paper from 2014, Itai Ben Yaacov considered complete valued fields, with value group in the reals, as structures in continuous logic, working with the projective line - a bounded metric space - instead of the valued field itself. He showed that the theory of algebraically closed metric non-trivially valued fields forms the model-companion of the corresponding theory. In the talk, I will present two recent results on metric valued fields of residue characteristic 0, namely a complete description of the elementary classes in terms of the residue field and value group (in a sense an approximate AKE principle), and the fact that, contrarily to the situation in discrete logic, the theory of metric valued fields with a distinguished isometric isomorphism does not admit a model-companion, answering a question of Ben Yaacov. This is joint work with Stefan Ludwig.

Speakers from the University of Münster

Hils, Martin

Professorship for Mathematical Logic (Prof. Hils)