Skip to main content

Quantifier elimination and decision procedures for valued fields

  • Conference paper
  • First Online:
Models and Sets

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1103))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J.Ax-S.Kochen, Diophantine problems over local fields I,II, Amer. J. Math. 87, 605–648.

    Google Scholar 

  2. — " —, Diophantine problems over local fields III, Annals of Math. 83, 437–456.

    Google Scholar 

  3. S.Baserab, Some model theory for henselian valued fields, J. of Algebra 55, 191–212.

    Google Scholar 

  4. —"—, A model theoretic transfer theorem for henselian valued fields, Crelle's Journal 311/312, 1–30.

    Google Scholar 

  5. 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. Th.Becker, Real closed rings and ordered valuation rings, Zeitschr. f. Math. Logik u. G. M. 29, 417–425.

    Google Scholar 

  7. M.Boffa, Unpublished manuscript.

    Google Scholar 

  8. S.S.Brown, Bounds on transfer principles for algebraically closed and complete discretely valued fields, Memoris AMS, vol. 204.

    Google Scholar 

  9. G.Cherlin-M.Dickmann, Real-closed rings II. Model Theory, Ann. of pure and appl. Logic 25, 213–231.

    Google Scholar 

  10. P.J.Cohen, Decision procedures for real and p-adic fields, Comm. pure and appl. Math. 22, 131–153.

    Google Scholar 

  11. F. Delon, Quelques proprietés des corps valués en théorie des modèles, Thèse, Paris.

    Google Scholar 

  12. J. Denef, The rationality of the Poincaré series associated to the p-adic points on a variety (Second version), preprint.

    Google Scholar 

  13. L.van den Dries, Model theory of Fields, thesis, Utrecht.

    Google Scholar 

  14. — " —, Quantifier elimination for linear formulas over ordered and valued fields, Bull.Soc.Math. Belg. 23, 19–32.

    Google Scholar 

  15. L.van den Dries, Algebraic theories with definable Skolem functions, preprint.

    Google Scholar 

  16. — " —, Elementary invariants for henselian valuation rings of mixed characteristic, and relative versions, manuscript, Jan. 1983.

    Google Scholar 

  17. P.Eklof-E.Fischer, The elementary theory of abelian groups, Ann. math. Logic 4, 115–171.

    Google Scholar 

  18. O.Endler, Valuation Theory, Springer, Berlin-Heidelberg.

    Google Scholar 

  19. 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. —"—, On the elementary theory of maximal normed fields, Sov. Math. Doklady 6, 1390–1393.

    Google Scholar 

  21. —"—, Multiply valued fields, Sov. Math. Doklady 22, 63–66.

    Google Scholar 

  22. M.J.Greenberg, Lectures on forms in many variables, Benjamin, New York.

    Google Scholar 

  23. S.Kochen, The model theory of local fields, Logic Conf. Kiel 1974, Springer LNM, vol. 499.

    Google Scholar 

  24. A.Macintyre, On definable sets of p-adic numbers, J. Symb. Logic 41, 605–610.

    Google Scholar 

  25. — " —, Model-completeness, in Handbook of math. Logic, North-Holland, Amsterdam, 139–180.

    Google Scholar 

  26. A.Macintyre-K.McKenna-L.v.d.Dries, Elimination of quantifiers in algebraic structures, Adv. in Math. 47, 74–87.

    Google Scholar 

  27. A.Nerode, A decision method for p-adic integral zeros of diophantine equations, Bull. AMS 69, 513–517.

    Google Scholar 

  28. A.Prestel-P.Roquette, Formally p-adic fields, Springer LNM, vol. 1050.

    Google Scholar 

  29. A.Robinson, Complete Theories, North-Holland, Amsterdam.

    Google Scholar 

  30. P.Roquette, Some tendencies in contemporary algebra, to appear.

    Google Scholar 

  31. V.Weispfenning, Elementary theories of valued fields, Dissertation, Universität Heidelberg.

    Google Scholar 

  32. — " —, On the elementary theory of Hensel fields, Ann. math. Logic 10, 59–93.

    Google Scholar 

  33. — " —, Model theory of lattice products, Habilitationsschrift, Universität Heidelberg

    Google Scholar 

  34. — " —, Quantifier elimination for certain ordered and lattice-ordered abelian groups, Bull. Soc. Math. Belg. 23, 131–156.

    Google Scholar 

  35. — " —, Valuation rings and boolean products, Proc. Conf. F.N.R.S., Brussels.

    Google Scholar 

  36. — " —, Aspects of quantifier elimination in algebra, to appear in Proc. Conf. Univ. Alg., Darmstadt 1983.

    Google Scholar 

  37. — " —, Quantifier elimination for ultrametric spaces, Abstract, Table ronde de logique, Paris 1983.

    Google Scholar 

  38. — " —, Some decidable second-order field theories, Abstract, Table ronde de logique, Paris 1983.

    Google Scholar 

  39. M.Ziegler, Die elementare Theorie henselscher Körper, Dissertation, Universität Köln.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Gert H. Müller Michael M. Richter

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Weispfenning, V. (1984). Quantifier elimination and decision procedures for valued fields. In: Müller, G.H., Richter, M.M. (eds) Models and Sets. Lecture Notes in Mathematics, vol 1103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099397

Download citation

  • DOI: https://doi.org/10.1007/BFb0099397

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13900-3

  • Online ISBN: 978-3-540-39115-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics