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.

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.

3) (Jensen's theorem): Let $\kappa$ be an inaccessible cardinals and let $B=RO(P),$ where $P=Col(\aleph_0, < \kappa).$ If $B_1, B_2$ are complete Boolean algebras of size $<\kappa$ such that $B_1$ is a sub-algebra of both $B$ and $B_1$, then there is an embedding $h$ of $B_2$ into $B$ such that $h\restriction B_1$ is the identity.