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Henselianity and the Denef-Pas language

  • Yimu Yin (a1)

Abstract

We prove that if an equicharacteristic valued field has a ℤ-group as its value group and admits quantifier elimination in the main sort of the prototypical Denef-Pas style language then it is henselian. In fact the proof of this suggests that a reasonable class of Denef-Pas style languages is natural with respect to henselianity.

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[1]Cluckers, Raf, Model theory of valued fields, Quaderni di matematica, vol. 11. pp. 7385, Quaderni di matematica, Dipartmento di Matematica della Seconda Università di Napoli, 2002, pp. 73–85.
[2]Dickmann, M. A., Elimination of quantifiers for ordered valuation rings, this Journal, vol. 52 (1987), pp. 116128.
[3]Engler, Antonio J. and Prestel, Alexander, Valued fields, Springer-Verlag, Berlin, 2005.
[4]Macintyre, Angus, On definable subsets of p-adic fields, this Journal, vol. 41 (1976), pp. 605610.
[5]Macintyre, Angus, McKenna, Kenneth, and van den Dries, Lou, Elimination of quantifiers in algebraic structures, Advances in Mathematics, vol. 47 (1983), pp. 7487.
[6]Pas, Johan, Uniform p-adic cell decomposition and local zeta functions. Journal für die reine und angewandte Mathematik, vol. 399 (1989), pp. 137172.
[7]Yin, Yimu, On logical characterization of henselianity. arXiv: 0705.0395.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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