The theorem of the complement for nested sub-Pfaffian sets
The theorem of the complement for nested sub-Pfaffian sets
复制标题
嵌套亚普法夫集的补集定理
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
P. Speissegger
中科院分区：
文献类型：
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作者：
J. Lion;P. Speissegger
Let R be an o-minimal expansion of the real field, and let
L(R) be the language consisting of all nested Rolle leaves over R. We call a set nested subpfaffian over R if it is the projection of a boolean combination of definable sets and nested Rolle leaves over R. Assuming that R admits analytic cell decomposition, we prove that the complement of a nested subpfaffian set over R is again a nested subpfaffian set over R. As a corollary, we obtain that if R admits analytic cell decomposition, then the pfaffian closure P(R) of R is obtained by adding to R all nested Rolle leaves over R, a one-stage process, and that P(R) is model complete in the language L(R).
