Cell decomposition for semibounded p-adic sets

作者：Leenknegt Eva^*

来源：Archive for Mathematical Logic, 2013, 52(5-6): 667-688.

DOI：10.1007/s00153-013-0337-8

• Cell decomposition
• Quantifier elimination
• p-adic numbers
• p-minimality
• o-minimality
• Definability
• Restricted multiplication

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.

• 出版日期2013-8