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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:liu@math.purdue.edu
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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

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References

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