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Given a Boolean algebra $A$, we construct another Boolean algebra $B$ with nouncountable well-ordered chains such that the Banach space of real valuedcontinuous functions $C(K_A)$ embeds isometrically into $C(K_B)$, where $K_A$and $K_B$ are the Stone spaces of $A$ and $B$ respectively. As a consequence weobtain the following: If there exists an isometrically universal Banach spacefor the class of Banach spaces of a given uncountable density $\kappa$, thenthere is another such space which is induced by a Boolean algebra which is notuniversal for Boolean algebras of cardinality $\kappa$. Such a phenomenoncannot happen on the level of separable Banach spaces and countable Booleanalgebras. This is related to the open question if the existence of anisometrically universal Banach space and of a universal Boolean algebra areequivalent on the nonseparable level (both are true on the separable level).

An isometrically universal Banach space induced by a non-universal Boolean algebra