Definable Henselian Valuation Rings

Prestel, Alexander

Definable Henselian Valuation Rings

Dateien

Prestel_0-319892.pdfGröße: 136.51 KBDownloads: 276

Datum

2015

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

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

Zusammenfassung

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.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

definability, valuation rings

Zitieren

ISO 690

PRESTEL, Alexander, 2015. Definable Henselian Valuation Rings. In: The Journal of Symbolic Logic. 2015, 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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