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Uniform definability of henselian valuation rings in the Macintyre language

Uniform definability of henselian valuation rings in the Macintyre language

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FEHM, Arno, Alexander PRESTEL, 2014. Uniform definability of henselian valuation rings in the Macintyre language

@unpublished{Fehm2014Unifo-29359, title={Uniform definability of henselian valuation rings in the Macintyre language}, year={2014}, author={Fehm, Arno and Prestel, Alexander} }

2014-12-01T10:08:10Z eng 2014-12-01T10:08:10Z Prestel, Alexander Fehm, Arno We discuss definability of henselian valuation rings in the Macintyre language L<sub>Mac</sub>, 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 ∃-∅-definable in L<sub>Mac</sub>, and henselian valuation rings with value group Z are uniformly ∃∀-∅-definable in the ring language, but not uniformly ∃-∅-definable in L<sub>Mac</sub>. We apply these results to local fields Q<sub>p</sub> and F<sub>p</sub>((t)), as well as to higher dimensional local fields. Uniform definability of henselian valuation rings in the Macintyre language 2014 Fehm, Arno Prestel, Alexander

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