Výsledky vyhledávání - "Mariaule, Nathanaël"

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Expansions of the $p$-adic numbers that interprets the ring of integers

Autor: Mariaule, Nathanaël

Let $\widetilde{\mathbb{Q}_p}$ be the field of $p$-adic numbers in the language of rings. In this paper we consider the theory of $\widetilde{\mathbb{Q}_p}$ expanded by two predicates interpreted by multiplicative subgroups $\alpha^\mathbb{Z}$ and $\

Externí odkaz: http://arxiv.org/abs/1905.11146

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Expansion of Presburger arithmetic with the exchange property

Autor: Mariaule, Nathanaël

Let $G$ be a model of Presburger arithmetic. Let $\mathcal{L}$ be an expansion of the language of Presburger $\mathcal{L}_{Pres}$. In this paper we prove that the $\mathcal{L}$-theory of $G$ is $\mathcal{L}_{Pres}$-minimal iff it has the exchange pro

Externí odkaz: http://arxiv.org/abs/1806.00315

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Model theory of the field of $p$-adic numbers expanded by a multiplicative subgroup

Autor: Mariaule, Nathanaël

Let $G$ be a multiplicative subgroup of $\mathbb{Q}_p$. In this paper, we describe the theory of the pair $(\mathbb{Q}_p, G)$ under the condition that $G$ satisfies Mann property and is small as subset of a first-order structure. First, we give an ax

Externí odkaz: http://arxiv.org/abs/1803.10564

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Dissertation/ Thesis

On the decidability of the p-adic exponential ring

Autor: Mariaule, Nathanaël

Let Zp be the ring of p-adic integers and Ep be the map x-->exp(px) where exp denotes the exponential map determined by the usual power series. It defines an exponential ring (Zp, +, ., 0, 1, Ep). The goal of the thesis is to study the model theory

Externí odkaz: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.606986

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p-adic exponential ring, p-adic Schanuel's conjecture and decidability

Autor: Mariaule, Nathanaël

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 to 2, we set E_2(x)=exp(4x)). Furthermore, E_p determines a structure o

Externí odkaz: http://arxiv.org/abs/1408.0900

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Effective model-completeness for p-adic analytic structures

Autor: Mariaule, Nathanaël

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 language of p-adic restricted analytic functions expanded by a division

Externí odkaz: http://arxiv.org/abs/1408.0610

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