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?



The continuum hypothesis and the diamond principle for $\aleph_1$
Jensen's diamond implies CH. See <https://math.stackexchange.com/a/2073421/17929>


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


