Linear O-minimal structures
Linear O-minimal structures
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线性 O-最小结构
DOI：
10.1007/bf02761295
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发表时间：
1993
影响因子：
1
通讯作者：
Y. Peterzil
中科院分区：
文献类型：
--
作者：
James Loveys;Y. Peterzil
抽象线性有序结构
$$\Mathcal{M}=(M，<；，\CDOT\CDOT\CDOT)$$
如果Fm的每个可定义子集都是点和区间的有限并，则称为o-极小。这样的一种
$$\数学{M}$$
是ACF结构，如果，粗略地说，每一个可定义的曲线族在局部是一个单参数曲线族。我们证明如果
$$\数学{M}$$
是扩展有序群(区间)的ACF结构，则它初等等价于有序向量空间(区间)的约化。在此过程中，我们证明了有序向量空间的展开和约化的几个量词消去结果。
AbstractA linearly ordered structure
$$\mathcal{M} = (M,< , \cdot \cdot \cdot )$$
is called o-minimal if every definable subset ofM is a finite union of points and intervals. Such an
$$\mathcal{M}$$
is aCF structure if, roughly said, every definable family of curves is locally a one-parameter family. We prove that if
$$\mathcal{M}$$
is aCF structure which expands an (interval in an) ordered group, then it is elementary equivalent to a reduct of an (interval in an) ordered vector space. Along the way we prove several quantifier-elimination results for expansions and reducts of ordered vector spaces.