Model theory for Cp-theorists

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.