Mathematical Sciences: Model Theory, Geometry and Arithmetic

本项目的第1部分是模型论、代数和几何 将继续发展p-adic和刚性理论 次解析集 p-adic理论是由Denef和货车提出的 德赖斯和严格的分析理论是由 调查员 这些发展是基于各种量词 消去定理 它也是为了给新的证据， 定理在真实的情况下使用这种方法的量词 消除和转移这些新的证明也对p-adic 和严格的分析案例。 调查与以下方面的联系 Artin逼近定理也被考虑。 项目第2部分将继续调查 各种丢番图的问题，在语言的补充和 整数环和多项式环的整除性。 这将 扩展了研究者Denef和Pheidas的早期工作。 很有趣的是，关于代数的定理 像幂级数环这样的对象可以被认真地处理， 从数学逻辑中得出的方法，也就是说， 主要涉及定理所用语言的特征， 表达了。 这不是故事的全部，但看看有多远 一个人可以通过这种方式将其他障碍物隔离在一个高度 启发的方式。

Part 1 of this project in model theory, algebra and geometry will continue the development of a theory of p-adic and rigid subanalytic sets. The p-adic theory was begun by Denef and van den Dries and the rigid analytic theory was developed by the investigator. These developments are based on various quantifier elimination theorems. It is also intended to give new proofs of theorems in the real case using this method of quantifier elimination and to transfer these new proofs also to the p-adic and rigid analytic cases. The investigation of connections with Artin Approximation Theorems is also contemplated. Section 2 of the project will continue the investigation of various diophantine problems in the language of addition and divisibility for the integers and polynomial rings. This would extend earlier work by the investigator, Denef and Pheidas. It is fascinating to see how theorems about algebraic objects such as rings of power series can be seriously addressed by methods drawn from mathematical logic, that is, methods which deal largely with features of the language in which the theorems are expressed. This is not the whole story, but seeing how far one can get in this way isolates other obstacles in a highly illuminating way.