Submission date: 2 May 2023

Abstract:

We give a characterization of ω-pseudo complete valued fields elementarily equivalent to a finite extension L of the p-adics and with a fixed value group G of cardinality ℵ_1 in terms of a Hahn-like construction over L, generalizing a result obtained by Ax J. and Kochen S. in '65 for formally p-adic fields. We extend this construction to a more general contest of mixed characteristic valued fields with finite ramification.

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Full text arXiv 2305.01635: pdf, ps.