Effective model-completeness for p-adic analytic structures

Nathanaël Mariaule

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arXiv · 1408.0610

Effective model-completeness for p-adic analytic structures

Nathanaël Mariaule

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Abstract

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 symbol. In this paper, we are interested in restriction of this language: Let F be any family of restricted analytic functions, we construct an expansion of F so that the theory of the ring of p-adic integers is model-complete in the corresponding language. Next, we give conditions on F so that the model-completeness is effective. Finally, we apply our results in the context of p-adic exponential rings.

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BibTeX RIS

Nathanaël Mariaule. 2014-08-04. Effective model-completeness for p-adic analytic structures. https://arxiv.org/abs/1408.0610

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