Countable Boolean algebras as subalgebras and homomorphs

Weak homomorphisms and invariants: an example

“…Day showed using topological methods that any two countable superatomic Boolean algebras with the same invariants are isomorphic. In [3], Cramer described a partial order <; on the Day invariants. He showed, again using topological methods, that the countable algebra A is embeddable in B if and only if the Day invariant of A is ^ the Day invariant of B f and that the countable algebra B is a homomorphic image of the countable algebra A if and only if the invariant of A is ^ the invariant of B.…”