Quantifier elimination and rectilinearization theorem for generalized quasianalytic algebras
Quantifier elimination and rectilinearization theorem for generalized quasianalytic algebras
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广义拟解析代数的量词消除和直线化定理
DOI：
10.1112/plms/pdv010
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发表时间：
2013
影响因子：
1.8
通讯作者：
Tamara Servi
中科院分区：
文献类型：
--
作者：
J. Rolin;Tamara Servi
对于每个n∈N，我们考虑连续真实的值函数在0∈Rn的芽代数An，使得我们可以将每个芽f∈An与具有非负真实的指数的（发散）级数T（f）相关联，这可以被认为是f的渐近展开。我们要求R-代数同态f <$T（f）是单射的（拟解析性质）。在这种情况下，我们证明了类似的结果Denef和货车登德里斯的量词消除定理和Hironaka的次解析集的直线化定理。
We consider for every n∈N an algebra An of germs at 0∈Rn of continuous real‐valued functions, such that we can associate to every germ f∈An a (divergent) series T(f) with non‐negative real exponents, which can be thought of as an asymptotic expansion of f . We require that the R ‐algebra homomorphism f↦T(f) be injective (quasianalyticity property). In this setting, we prove analogue results to Denef and van den Dries’ quantifier elimination theorem and Hironaka's rectilinearization theorem for subanalytic sets.