论文标题
非优质分类和投影本地O-Wimimal类
Non-elementary categoricity and projective locally o-minimal classes
论文作者
论文摘要
给定一个封面的$ \ mathbb {u} $是一个光滑的复杂代数品种的家族，我们将其与$ \ mathcal {u}相关联，$ contecal of o-Minals在o-Minimal the Reals中均可在本地定义的结构。我们证明该类是$ \ aleph_0 $ - homepoin，而不是子模型和稳定。因此，$ \ Mathcal {u} $在基数$ \ aleph_1中是绝对的。
Given a cover $\mathbb{U}$ of a family of smooth complex algebraic varieties, we associate with it a class $\mathcal{U},$ containing $\mathbb{U}$, of structures locally definable in an o-minimal expansion of the reals. We prove that the class is $\aleph_0$-homogenous over submodels and stable. It follows that $\mathcal{U}$ is categorical in cardinality $\aleph_1.$ In the one-dimensional case we prove that a slight modification of $\mathcal{U}$ is an abstract elementary class categorical in all uncountable cardinals.
