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Let me say a few such examples:

1. (Kripke's theorem): For every Boolean lagebra $B$, there is a cardinal $\kappa$ such that $B$ can be embedded in the collapsing algebra $Col(\aleph_0, \kappa).$

2. (Solovay's theorem) Let $B$ be a Souslin algebra. Then $|B|\leq 2^{\aleph_1}$ (see Jech 1978, Theorem 60, page 274).

In fact most of section 25 ``Forcing and complete Boolean algebras'' of Jech 1978, gives such examples.