论文标题
部分可观测时空混沌系统的无模型预测
Spectral Spaces in o-minimal and other NIP theories
论文作者
论文摘要
我们通过光谱拓扑研究了一些模型理论概念。在O最低设置中，我们将O-Wimimal Spectrum与其他拓扑空间（例如真实的光谱和无穷小型彼得齐尔和Starchenko的空间）联系起来。特别是，我们证明，对于绝对紧凑的组，封闭点的空间对于无穷小型类型的空间是同构的。我们还证明，使用频谱拓扑结构，集中在紧凑的集合中的不变类型的集合是正常的光谱空间，其封闭点是有限令人满意的类型。 另一方面，对于任意的nip结构，我们为一组不变类型装备了一个新拓扑，称为{\ em诚实拓扑}。有了这种拓扑结构，不变类型的集合是一个普通的光谱空间，其封闭点是有限的令人满意的点，并且从不变类型中的自然缩回到有限令人满意的类型上，与Simon的$ f_m $撤回相吻合。
We study some model-theoretic notions in NIP by means of spectral topology. In the o-minimal setting we relate the o-minimal spectrum with other topological spaces such as the real spectrum and the space of infinitesimal types of Peterzil and Starchenko. In particular, we prove for definably compact groups that the space of closed points is homeomorphic to the space of infinitesimal types. We also prove that with the spectral topology the set of invariant types concentrated in a definably compact set is a normal spectral space whose closed points are the finitely satisfiable types. On the other hand, for arbitrary NIP structures we equip the set of invariant types with a new topology, called the {\em honest topology}. With this topology the set of invariant types is a normal spectral space whose closed points are the finitely satisfiable ones, and the natural retraction from invariant types onto finitely satisfiable types coincides with Simon's $F_M$ retraction.
