Submission date: 8 January 2014.

Abstract:

In these notes, we prove field quantifier elimination for valued fields with both analytic structure and an isometry that are σ-Henselian and have enough constants. From this result we can deduce various Ax-Kochen-Ersov type results both for completeness and for the NIP property. The main example we are interested in are the Witt vectors on the algebraic closure of F_p with their natural analytic structure and the lifting of the Frobenius. It turns out we can give a (reasonable) axiomatization of their first order theory and that this theory is NIP.

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Full text arXiv 1401.1765: pdf, ps.