Locally polynomially bounded structures
Locally polynomially bounded structures
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局部多项式有界结构
DOI：
10.1112/blms/bdn004
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发表时间：
2007
影响因子：
0.9
通讯作者：
A. Wilkie
中科院分区：
文献类型：
--
作者：
G. Jones;A. Wilkie
我们证明了一个定理，它提供了一种在由某些平滑函数定义的品种上构造点的方法。我们要求函数可以在实闭域的可定义完全展开中定义，并且可以在固定的最小和多项式有界约简中局部定义。作为一个应用，我们证明在某些最小结构中，可定义函数是在语言中的基本函数上分段隐式定义的。
We prove a theorem which provides a method for constructing points on varieties defined by certain smooth functions. We require that the functions be definable in a definably complete expansion of a real closed field and be locally definable in a fixed o‐minimal and polynomially bounded reduct. As an application we show that in certain o‐minimal structures, definable functions are piecewise implicitly defined over the basic functions in the language.