Quantifier elimination and decision procedures for valued fields

  • Volker Weispfenning
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1103)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 65.
    J.Ax-S.Kochen, Diophantine problems over local fields I,II, Amer. J. Math. 87, 605–648.Google Scholar
  2. 66.
    — " —, Diophantine problems over local fields III, Annals of Math. 83, 437–456.Google Scholar
  3. 78.
    S.Baserab, Some model theory for henselian valued fields, J. of Algebra 55, 191–212.Google Scholar
  4. 79.
    —"—, A model theoretic transfer theorem for henselian valued fields, Crelle's Journal 311/312, 1–30.Google Scholar
  5. 80.
    J.Becker-J.Denef-L.Lipshitz, Further remarks on the elementary theory of formal power series, in Model Theory of Algebra and Arithmetic, Proc. Karpacz 1979, Springer LNM vol. 834.Google Scholar
  6. 83.
    Th.Becker, Real closed rings and ordered valuation rings, Zeitschr. f. Math. Logik u. G. M. 29, 417–425.Google Scholar
  7. 80a.
    M.Boffa, Unpublished manuscript.Google Scholar
  8. 78.
    S.S.Brown, Bounds on transfer principles for algebraically closed and complete discretely valued fields, Memoris AMS, vol. 204.Google Scholar
  9. 83.
    G.Cherlin-M.Dickmann, Real-closed rings II. Model Theory, Ann. of pure and appl. Logic 25, 213–231.Google Scholar
  10. 69.
    P.J.Cohen, Decision procedures for real and p-adic fields, Comm. pure and appl. Math. 22, 131–153.Google Scholar
  11. 81.
    F. Delon, Quelques proprietés des corps valués en théorie des modèles, Thèse, Paris.Google Scholar
  12. 81a.
    J. Denef, The rationality of the Poincaré series associated to the p-adic points on a variety (Second version), preprint.Google Scholar
  13. 78.
    L.van den Dries, Model theory of Fields, thesis, Utrecht.Google Scholar
  14. 81.
    — " —, Quantifier elimination for linear formulas over ordered and valued fields, Bull.Soc.Math. Belg. 23, 19–32.Google Scholar
  15. a.
    L.van den Dries, Algebraic theories with definable Skolem functions, preprint.Google Scholar
  16. b.
    — " —, Elementary invariants for henselian valuation rings of mixed characteristic, and relative versions, manuscript, Jan. 1983.Google Scholar
  17. 72.
    P.Eklof-E.Fischer, The elementary theory of abelian groups, Ann. math. Logic 4, 115–171.Google Scholar
  18. 72.
    O.Endler, Valuation Theory, Springer, Berlin-Heidelberg.Google Scholar
  19. 65–67.
    Ju.Ersov, On the elementary theory of maximal valued fields (russian), Algebra i Logika I: 4, 31–69, II: 5, 8–40, III: 6, 31–73.Google Scholar
  20. 65.
    —"—, On the elementary theory of maximal normed fields, Sov. Math. Doklady 6, 1390–1393.Google Scholar
  21. 80.
    —"—, Multiply valued fields, Sov. Math. Doklady 22, 63–66.Google Scholar
  22. 69.
    M.J.Greenberg, Lectures on forms in many variables, Benjamin, New York.Google Scholar
  23. 75.
    S.Kochen, The model theory of local fields, Logic Conf. Kiel 1974, Springer LNM, vol. 499.Google Scholar
  24. 76.
    A.Macintyre, On definable sets of p-adic numbers, J. Symb. Logic 41, 605–610.Google Scholar
  25. 77.
    — " —, Model-completeness, in Handbook of math. Logic, North-Holland, Amsterdam, 139–180.Google Scholar
  26. 83.
    A.Macintyre-K.McKenna-L.v.d.Dries, Elimination of quantifiers in algebraic structures, Adv. in Math. 47, 74–87.Google Scholar
  27. 63.
    A.Nerode, A decision method for p-adic integral zeros of diophantine equations, Bull. AMS 69, 513–517.Google Scholar
  28. 83.
    A.Prestel-P.Roquette, Formally p-adic fields, Springer LNM, vol. 1050.Google Scholar
  29. 56.
    A.Robinson, Complete Theories, North-Holland, Amsterdam.Google Scholar
  30. 56a.
    P.Roquette, Some tendencies in contemporary algebra, to appear.Google Scholar
  31. 71.
    V.Weispfenning, Elementary theories of valued fields, Dissertation, Universität Heidelberg.Google Scholar
  32. 76.
    — " —, On the elementary theory of Hensel fields, Ann. math. Logic 10, 59–93.Google Scholar
  33. 78.
    — " —, Model theory of lattice products, Habilitationsschrift, Universität HeidelbergGoogle Scholar
  34. 81.
    — " —, Quantifier elimination for certain ordered and lattice-ordered abelian groups, Bull. Soc. Math. Belg. 23, 131–156.Google Scholar
  35. 82.
    — " —, Valuation rings and boolean products, Proc. Conf. F.N.R.S., Brussels.Google Scholar
  36. a.
    — " —, Aspects of quantifier elimination in algebra, to appear in Proc. Conf. Univ. Alg., Darmstadt 1983.Google Scholar
  37. b.
    — " —, Quantifier elimination for ultrametric spaces, Abstract, Table ronde de logique, Paris 1983.Google Scholar
  38. c.
    — " —, Some decidable second-order field theories, Abstract, Table ronde de logique, Paris 1983.Google Scholar
  39. 72.
    M.Ziegler, Die elementare Theorie henselscher Körper, Dissertation, Universität Köln.Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Volker Weispfenning
    • 1
  1. 1.University of HeidelbergGermany

Personalised recommendations