Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-13T00:47:09.475Z Has data issue: false hasContentIssue false
  • English
  • Français

Semilinear cell decomposition

Published online by Cambridge University Press:  12 March 2014

Nianzheng Liu
Nianzheng Liu*
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907,, E-mail:[email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We obtain a p-adic semilinear cell decomposition theorem using methods developed by Denef in [Journal für die Reine und Angewandte Mathematik, vol. 369 (1986), pp. 154–166]. We also prove that any set definable with quantifiers in (0,1, +, —, λq, Pn){n∈ℕ,q∈ℚp} may be defined without quantifiers, where λq is scalar multiplication by q and Pn is a unary predicate which denotes the nonzero nth powers in the p-adic field ℚp. Such a set is called a p-adic semilinear set in this paper. Some further considerations are discussed in the last section.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 1 , March 1994 , pp. 199 - 208
Copyright
Copyright © Association for Symbolic Logic 1994

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

[D]Denef, J., p-Adic semi-algebraic sets and cell decomposition, Journal für die Reine und Angewandte Mathematik, vol. 369 (1986), pp. 154–166.Google Scholar
[Dub]Dubhashi, D., Algorithmic investigations in p-adic fields, Ph.D. Thesis, Department of Computer Science, Cornell University, Ithaca, NY, 09, 1992.Google Scholar
[vdD]van den Dries, L., Quantifier elimination for linear formulas over ordered and valued fields, Bulletin de la Société Mathématique de Belgique, vol. 23 (1981), pp. 19–32.Google Scholar
[Liu]Liu, N., Analytic cell decomposition and the closure of p-adic semianalytic sets, preprint.Google Scholar
[M]Macintyre, A., On definable subsets of p-adic fields, this Journal, vol. 41 (1976), pp. 605–610.Google Scholar
[MPP]Marker, D., Peterzil, Y., and Pillay, A., Additive reducts of real closed fields, this Journal, vol. 57 (1992), pp. 109–117.Google Scholar
[PSS]Pillay, A., Scowcroft, P., and Steinhorn, C., Between groups and rings, The Rocky Mountain Journal of Mathematics, vol. 19 (1989), pp. 871–885.CrossRefGoogle Scholar
[SD]Scowcroft, P. and van den Dries, L., On the structure of semialgebraic sets over p-adic fields, this Journal, vol. 53 (1988), pp. 1138–1164.Google Scholar
[W]Weispfenning, W., Quantifier elimination and decision procedures for valued fields, Models and Sets, Lecture Notes in Mathematics, vol. 1103, Springer-Verlag, New York, 1984, pp. 419–472.Google Scholar