科研之友
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摘要
We discuss definability of henselian valuation rings in the Macintyre language L-Mac, the language of rings expanded by nth power predicates. In particular, we show that henselian valuation rings with finite or Hilbertian residue field are uniformly there exists-empty set- definable in L-Mac, and henselian valuation rings with value group Z are uniformly there exists for all-empty set- definable in the ring language, but not uniformly there exists-empty set-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.
- 出版日期2015-8
