Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-25T19:41:59.720Z Has data issue: false hasContentIssue false
  • English
  • Français

A model complete theory of valued D-fields

Published online by Cambridge University Press:  12 March 2014

Thomas Scanlon
Thomas Scanlon*
Affiliation:
University of California, Berkeley, Department of Mathematics, Evans Hall #3840, Berkeley, California 94720-3840, USA, E-mail:scanlon@math.berkeley.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

The notion of a D-ring, generalizing that of a differential or a differenee ring, is introduced, Quantifier elimination and a version of the Ax—Kochen—Eršov principle is proven for a theory of valued D-fields of residual characteristic zero.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 4 , December 2000 , pp. 1758 - 1784
Copyright
Copyright © Association for Symbolic Logic 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Ax, J. and Kochen, S., Diophantine problems over local fields I, American Journal of Mathematics, vol. 87 (1965), pp. 605–630.CrossRefGoogle Scholar
[2]Chang, C.C. and Keisler, J., Model theory, 3rd ed., North-Holland, 1990.Google Scholar
[3]Chatzidakis, Z. and Hrushovski, E., The model theory of difference fields, Transactions of the American Mathematical Society, vol. 351 (1999), no. 8, pp. 2997–3071.CrossRefGoogle Scholar
[4]Endler, O., Valuation theory, Universitext, Spinger-Verlag, Berlin, 1972.CrossRefGoogle Scholar
[5]Hodges, W., Model theory, Encyclopedia of Mathematics and its Applications, vol. 42, Cambridge University Press, Cambridge, 1993.CrossRefGoogle Scholar
[6]Kuhlmann, F.-V., On local uniformization in arbitrary characteristic, Fields Institute Preprint Series (Toronto). July 1997.Google Scholar
[7]Marker, D., Model theory of differential fields, Model theory of groups. Lecture notes in logic, vol. 5, Springer-Verlag, New York.Google Scholar
[8]Michaux, C., Ph.D. thesis, UniversitÉ Paris VII, 1991.Google Scholar
[9]Neumann, B., On ordered division rings, Transacton of the American Mathematical Society, vol. 66 (1949), pp. 202–252.CrossRefGoogle Scholar
[10]Raynaud, M., Anneaux locaux hensÉliens, Lecture notes in mathematics, vol. 169, Springer-Verlag, Berlin-NewYork, 1970.CrossRefGoogle Scholar
[11]Scanlon, T., Quantifier elimination for the relative Frobenius, preprint, 2000.Google Scholar
[12]Scanlon, T., Model theory of valued D-fields, Ph.D. thesis, Harvard University, May 1997.Google Scholar
[13]Schilling, O.F.G., The theory of valuations, American Mathematical Society Mathematical Survey, vol. 4, 1950.CrossRefGoogle Scholar
[14]Weispfenning, V., Quantifier eliminable ordered abelian groups, Algebra and order (Luminy-Marseille, 1984), R & E Res. Exp. Math., vol. 14, Heldermann, Berlin, 1986, pp. 113–126.Google Scholar