Submission date: 18 May 2012.

Abstract:

We study a reduct L_* of the ring language where multiplication is restricted to a neighbourhood of zero. The language is chosen such that for p-adically closed fields K, the L_*-definable subsets of K coincide with the semi-algebraic subsets of K. Hence structures (K,L_*) can be seen as the p-adic counterpart of the o-minimal structure of semibounded sets. We show that in this language, p-adically closed fields admit cell decomposition, using cells similar to p-adic semi-algebraic cells. From this we can derive quantifier-elimination, and give a characterization of definable functions. In particular, we conclude that multiplication can only be defined on bounded sets, and we consider the existence of definable Skolem functions.

Mathematics Subject Classification: 03C07, 03C10, 03C64, 11U09

Keywords and phrases:

Full text arXiv 1205.4178: pdf, ps.