A characterization of saturated models of a finite extension of the $p$-adics through a Hahn-like construction

Anna De Mase

Published 2023-05-02Version 1

We give a characterization of $\omega$-pseudo complete valued fields elementarily equivalent to a finite extension $L$ of the $p$-adics and with a fixed value group $G$ of cardinality $\aleph_{1}$ 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.