August 16, 2025

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

Key Points

This work characterizes finitely ramified pseudo complete valued fields, establishing connections to Hahn-like constructions.
Key evidence includes demonstrating these relationships under the Continuum Hypothesis, enhancing theoretical understanding.
The analysis builds on previous findings regarding unramified valued fields and extends them to mixed characteristic scenarios.
Implications point to enriched frameworks for studying valued fields, potentially impacting field theory and algebra.

Abstract

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.

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

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Abstract

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