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Preprint Number 2234

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2234. Martin Hils and Stefan Marian Ludwig
An Approximate AKE Principle for Metric Valued Fields

Submission date: 22 August 2022


We study metric valued fields in continuous logic, following Ben Yaacov's approach, thus working in the metric space given by the projective line. As our main result, we obtain an approximate Ax-Kochen-Ershov principle in this framework, completely describing elementary equivalence in equicharacteristic 0 in terms of the residue field and value group. Moreover, we show that, in any characteristic, the theory of metric valued difference fields does not admit a model-companion. This answers a question of Ben Yaacov.

Mathematics Subject Classification: 03C66, 03C60 (Primary), 12L10 (Secondary)

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Full text arXiv 2208.10186: pdf, ps.

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