We introduce a new class of separable Banach spaces, possibly being of interest to logicians, hereafter called guarded Fraïssé Banach spaces. The motivation comes from two directions:
(1) They generalize the class of Fraïssé Banach spaces recently introduced by Ferenczi, Lopez-Abad, Mbombo and Todorcevic which itself is motivated by both the notion of a Fraïssé structure from model theory as well as by the Banach spaces satisfying a relaxed version of the Mazur rotation problem.
(2) From a descriptive set theoretic point of view, they have the simplest definition up to isometry; namely, they are exactly the spaces whose isometry class is G_delta in a certain Polish space.
This class, in contrast to Fraïssé Banach spaces, seems to admit a large number of examples and is closely related to omega-categorical Banach spaces. Joint work with Marek Cúth and Noé de Rancourt.
