Generic Banach spaces and generic simplexes (Q642510)

The authors use ideas from mathematical logic to construct Banach spaces and simplexes. They use a notion of \textit{forcing} (namely here conditions which will give finite approximations to a forthcoming norm), a notion of \textit{unavoidable configurations} of norms, and a notion of \textit{amalgamation} of finite-dimensional spaces to construct a number of non-separable (they have density \(\omega_1\)) Banach spaces (hereditarily Lindelöf property, polyhedral, ``exact'' Schauder basis constant) or simplexes (Poulsen simplexes, Bauer simplexes), with specific other properties.