Definability in p-adic power series rings.

摘要

We prove the definability of a certain subset of Zmp . In particular, we show that the set of parameters x ∈ Zmp for which a homogeneous linear system over p-adic power series of the form f (x, Y) has a solution, is quantifier-free definable in the language of p-adic fields with restricted analytic functions. Furthermore, we show how to obtain a generating set for the solution space which is piecewise uniform in the parameters x ∈ Zmp .