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In [S. Shelah. Uncountable constructions for B.A. e.c. groups and Banach spaces. Israel J. Math. 51 (1985), 273-297], the existence of a special Banach space is proved, assuming the diamond principle for $\aleph_1$.

Is this diamond principle for $\aleph_1$ compatible with the continuum hypothesis?

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    $\begingroup$ I think that usually the first thing people learn about diamond is that it implies CH. Even before its consistency. $\endgroup$
    – Asaf Karagila ♦
    Commented Nov 5, 2018 at 14:04

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Jensen's diamond implies CH. See https://math.stackexchange.com/a/2073421/17929

https://en.wikipedia.org/wiki/Diamond_principle

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