Abstract 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.

中文翻译：

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Cp 理论家的模型理论

摘要 我们调查了与一般拓扑学有重要联系的离散和连续模型论概念。在 P. Casazza 和 J. Iovino 最近获得的关于紧凑连续的结果之后，我们对连续逻辑和 C p 理论之间的几种相互作用进行了独立的阐述，这些相互作用适用于涉及不包括 c 0 或 lp 的巴拿赫空间的分类问题逻辑。使用涉及 Grothendieck 空间和双极限条件的 C p 理论结果，我们将它们的结果扩展到更广泛的逻辑系列，即具有第一个可数弱 Grothendieck 类型空间的逻辑。我们提出了具有模型理论含义的 C p 理论问题。