p-adic解析结构的有效模型完全性
Effective model-completeness for p-adic analytic structures
摘要：
Denef和L.范登德里斯证明，理论的环的p-adic整数承认量词消去的语言的p-adic限制解析函数扩大了一个部门的象征。本文对这种语言的限制性进行了研究：设F是任意一族受限制的解析函数，我们构造了F的一个展开式，使得p-adic整数环理论在相应的语言中是模型完备的。其次，我们给出了F上的条件，使得模型完全性是有效的。最后，我们应用我们的结果的上下文中的p-adic指数环。
英文摘要：
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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