Atom of a Boolean algebra ($a>0,\nexists b(0<b<a)$)

An atom is a minimal nonzero Boolean-algebra element. In a Lindenbaum algebra, its nonempty formula class isolates a complete type. A finite Boolean algebra is the power set of its finite atom set. An infinite atomic Boolean algebra need not contain every union of atoms: the finite-cofinite algebra is a simple counterexample.