ABSTRACT We give a characterization of finitely ramified -pseudo complete valued fields of mixed characteristic (0, p), with fixed residue field k and value group G of cardinality ₁ in terms of a Hahn-like construction over the Cohen field C (k), modulo the Continuum Hypothesis. This is a generalization of results due to Ax and Kochen in ’65 for formally p-adic fields and by Kochen in ’74 for unramified valued fields with perfect residue field. We consider a more general context of finitely ramified valued fields of mixed characteristic with arbitrary residue field and a cross-section.
Anna De Mase (Wed,) studied this question.