A Characterization of Pseudo Complete Finitely Ramified Valued Fields Through a Hahn-Like Construction

We give a characterization of finitely ramified ω-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.