5 citations · 7 across the 5 of their papers we have counts for
5 papers
Expansions of the -adic numbers that interprets the ring of integers
Nathanaël Mariaule
Let be the field of -adic numbers in the language of rings. In this paper we consider the theory of expanded by two predica…
Expansion of Presburger arithmetic with the exchange property
Nathanaël Mariaule
Let be a model of Presburger arithmetic. Let be an expansion of the language of Presburger . In this paper we prove that the -the…
Model theory of the field of -adic numbers expanded by a multiplicative subgroup
Nathanaël Mariaule
Let be a multiplicative subgroup of . In this paper, we describe the theory of the pair under the condition that satisfies Mann property a…
p-adic exponential ring, p-adic Schanuel's conjecture and decidability
Nathanaël Mariaule
Let exp(x) be the function determined by the classical power series of the exponentiation. Then E_p(x):=exp(px) is well-defined on Zp, the ring of p-adic integer (for p not equal t…
Effective model-completeness for p-adic analytic structures
Nathanaël Mariaule
In their paper 'p-adic and real subanalytic sets, J. Denef and L. van den Dries prove that the theory of the ring of p-adic integers admits the elimination of quantifiers in the la…