An old question in Functional Analysis inquired whether there is a Banach space that does not contain a copy of either lp or c0. Tsirelson defined such a space through an infinitary process that inspired many other constructions of pathological spaces. Then Gowers popularized the problem: does every explicitly definable infinite dimensional Banach space contain a copy of lp or c0? In first-order logic, the notion of explicit definability is closely related to that of stability, which has been a driving force of Model Theory in the last decades since Shelah introduced the idea. We will discuss how these concepts extend to continuous logics in order to present Casazza and Iovino's positive answer to Gowers's question in finitary continuous logic and our current work around this result in infinitary continuous logics using Cp-theoretic tools.