Complements of subanalytic sets and existential formulas for analytic functions
Complements of subanalytic sets and existential formulas for analytic functions
复制标题
亚解析集的补集和解析函数的存在公式
DOI：
10.1007/s002220050066
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发表时间：
1996
影响因子：
3.1
通讯作者：
A. Gabrielov
中科院分区：
文献类型：
--
作者：
A. Gabrielov
摘要证明了由微分闭子代数上的实解析函数所定义的子解析集的补是由同一子代数上的函数所定义的子解析集。这个结果在逻辑中有一个等价的表述：考虑一个由上述使用等式和不等式以及存在量词和全称量词的函数构建的表达式。这样的表达式等价于涉及同一类函数的存在表达式，只要变量既不接近无穷也不接近定义域的边界。
AbstractWe show that the complement of a subanalytic set defined by real analytic functions from any subalgebra closed under differentiation is a subanalytic set defined by the functions from the same subalgebra. This result has an equivalent formulation in logic: Consider an expression built from functions as above using equalities and inequalities as well as existential and universal quantifiers. Such an expression is equivalent to an existential expression involving functions from the same class, provided that the variables approach neither infinity nor the boundary of the domain.