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THE FIELD OF p-ADIC NUMBERS WITH A PREDICATE FOR THE POWERS OF AN INTEGER

Published online by Cambridge University Press:  21 March 2017

NATHANAËL MARIAULE
NATHANAËL MARIAULE*
Affiliation:
INSTITUT DE MATHÉMATIQUES DE JUSSIEU - PARIS RIVE GAUCHE UNIVERSITÉ PARIS DIDEROT 75205 PARIS CEDEX 13, FRANCEE-mail: nathanael.mariaule@imj-prg.fr
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Abstract

In this paper, we prove the decidability of the theory of ℚp in the language (+, −,⋅, 0, 1, Pn(n ∈ ℕ)) expanded by a predicate for the multiplicative subgroup nℤ (where n is a fixed integer). There are two cases: if $v_p \left( n \right) > 0$ then the group determines a cross-section and we get an axiomatization of the theory and a result of quantifier elimination. If $v_p \left( n \right) = 0$, then we use the Mann property of the group to get an axiomatization of the theory.

Keywords

p-adically closed fieldsexpansion of valued fields
Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 1 , March 2017 , pp. 166 - 182
Copyright
Copyright © The Association for Symbolic Logic 2017 

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References

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