论文标题
$ C_P $的模型理论 - 理论家
Model Theory for $C_p$-theorists
论文作者
论文摘要
我们调查与一般拓扑具有重要联系的离散和连续模型理论概念。我们提出了连续逻辑和$ C_P $ - 理论之间的几种相互作用的独立阐述，这些逻辑与涉及Banach空间的分类问题有应用，该问题不包括$ C_0 $或$ L^p $，此前P. Casazza和J. Iovino获得了紧凑型逻辑的最新结果。我们使用$ C_P $ - 理论结果涉及Grothendieck空间和双重限制条件，我们将其结果扩展到更广泛的逻辑系列，即那些具有第一个可计数弱的类型空间的逻辑。我们提出$ C_P $ - 具有模型理论含义的理论问题。
We survey discrete and continuous model-theoretic notions which have important connections to general topology. We present a self-contained exposition of several interactions between continuous logic and $C_p$-theory which have applications to a classification problem involving Banach spaces not including $c_0$ or $l^p$, following recent results obtained by P. Casazza and J. Iovino for compact continuous logics. Using $C_p$-theoretic results involving Grothendieck spaces and double limit conditions, we extend their results to a broader family of logics, namely those with a first countable weakly Grothendieck space of types. We pose $C_p$-theoretic problems which have model-theoretic implications.
