Definable Henselian Valuation Rings

Prestel, Alexander

Definable Henselian Valuation Rings

Files

Prestel_0-319892.pdf(136.51 KB)

Date

2015

Publication type

Journal article

Publication status

Published

Published in

The Journal of Symbolic Logic ; 80 (2015), 04. - pp. 1260-1267. - ISSN 0022-4812. - eISSN 1943-5886

Abstract

We give model theoretic criteria for the existence of ∃∀ and ∀∃- formulas in the ring language to define uniformly the valuation rings O of models (K,O) of an elementary theory Σ of henselian valued fields. As one of the applications we obtain the existence of an ∃∀-formula defining uniformly the valuation rings O of valued henselian fields (K,O) whose residue class field k is finite, pseudofinite, or hilbertian. We also obtain ∀∃-formulas φ2 and φ4 such that φ2 defines uniformly k[[t]] in k(t) whenever k is finite or the function field of a real or complex curve, and φ4 replaces φ2 if k is any number field.

Subject (DDC)

510 Mathematics

Keywords

definability, valuation rings

Cite This

ISO 690

PRESTEL, Alexander, 2015. Definable Henselian Valuation Rings. In: The Journal of Symbolic Logic. 80(04), pp. 1260-1267. ISSN 0022-4812. eISSN 1943-5886. Available under: doi: 10.1017/jsl.2014.52

BibTex

@article{Prestel2015Defin-32915,
  year={2015},
  doi={10.1017/jsl.2014.52},
  title={Definable Henselian Valuation Rings},
  number={04},
  volume={80},
  issn={0022-4812},
  journal={The Journal of Symbolic Logic},
  pages={1260--1267},
  author={Prestel, Alexander}
}

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Bibliography of Konstanz

Yes