当前位置: X-MOL 学术Q. J. Math. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
On Local definability of holomorphic functions
Quarterly Journal of Mathematics ( IF 0.7 ) Pub Date : 2019-07-16 , DOI: 10.1093/qmath/haz015
Gareth Jones 1 , Jonathan Kirby 2 , Olivier Le Gal 3 , Tamara Servi 4
Affiliation  

Given a collection $\mathcal {A}$ of holomorphic functions, we consider how to describe all the holomorphic functions locally definable from $\mathcal {A}$. The notion of local definability of holomorphic functions was introduced by Wilkie, who gave a complete description of all functions locally definable from $\mathcal {A}$ in the neighbourhood of a generic point. We prove that this description is no longer complete in the neighbourhood of non-generic points. More precisely, we produce three examples of holomorphic functions that suggest that at least three new operations need to be added to Wilkie’s description in order to capture local definability in its entirety. The constructions illustrate the interaction between resolution of singularities and definability in the o-minimal setting.

中文翻译:

全纯函数的局部可定性

给定全纯函数的集合\ mathcal {A} $,我们考虑如何描述可从$ \ mathcal {A} $局部定义的所有全纯函数。Wilkie引入了全纯函数的局部可定义性的概念,他对从通用点附近的$ \ mathcal {A} $可局部定义的所有函数进行了完整描述。我们证明该描述在非通用点附近不再完整。更准确地说,我们提供了三个全纯函数的示例,这些示例表明至少需要在Wilkie的描述中添加三个新操作,才能完整地捕获局部可定义性。这些构造说明了奇异分辨率与o最小设置中的可定义性之间的相互作用。
更新日期:2020-01-04
down
wechat
bug