Submission date: 20 August 2014

Abstract:

We discuss definability of henselian valuation rings in the Macintyre language L_{Mac}, the language of rings expanded by n-th power predicates. In particular, we show that henselian valuation rings with finite or Hilbertian residue field are uniformly \exists-\emptyset-definable in L_{Mac}, and henselian valuation rings with value group Z are uniformly \exists\forall-\emptyset-definable in the ring language, but not uniformly \exists-\emptyset-definable in L_{Mac}. We apply these results to local fields Q_p and F_p((t)), as well as to higher dimensional local fields.

Mathematics Subject Classification: 03C60, 12L12, 12E30, 12J10

Keywords and phrases:

Full text arXiv 1408.4816: pdf, ps.