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We study certain Banach spaces that are added in the extension by one Cohen real. Specifically, we show that adding just one Cohen real to any model adds a Banach space of density ℵ1 which does not embed into any such space in the ground model (Theorem 1.1). Moreover, such a Banach space can be chosen to be UG (Theorem 1.6). This has consequences on the isomorphic universality number for Banach spaces...
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