特征序列中的持久性和NIP
Persistence and NIP in the characteristic sequence
摘要：
对于一个一阶公式$ϕ(x;y)$，引入并研究了由$P_n(y_1,...,y_n) := (\exists x) \bigwedge_{i \leq n} ϕ(x;y_i)$定义的超图的特征序列$<P_n : n < ω>$.我们表明，组合和分类理论的特性的特征序列反映分类理论的性质的$ϕ$，反之亦然。具体来说，我们发现，一些树的属性检测的存在下，某些组合配置的特征序列，而其他属性，如不稳定性和独立性表现在本地化的复杂配置的持久性。
英文摘要：
For a first-order formula $ϕ(x;y)$ we introduce and study the characteristic sequence $<P_n : n < ω>$ of hypergraphs defined by $P_n(y_1,...,y_n) := (\exists x) \bigwedge_{i \leq n} ϕ(x;y_i)$. We show that combinatorial and classification theoretic properties of the characteristic sequence reflect classification theoretic properties of $ϕ$ and vice versa. Specifically, we show that some tree properties are detected by the presence of certain combinatorial configurations in the characteristic sequence while other properties such as instability and the independence property manifest themselves in the persistence of complicated configurations under localization.
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