Effective model-completeness for p-adic analytic structures
Logic
2017-02-02 v2
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.
Keywords
Cite
@article{arxiv.1408.0610,
title = {Effective model-completeness for p-adic analytic structures},
author = {Nathanaël Mariaule},
journal= {arXiv preprint arXiv:1408.0610},
year = {2017}
}