= Atom of a Boolean algebra
{title2=$a>0,\quad\nexists b\ (0<b<a)$}
An <atom of a Boolean algebra>[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 of a Boolean algebra>[atom] <set>. An infinite atomic <Boolean algebra> need not contain every <union> of <atom of a Boolean algebra>[atoms]: the <finite-cofinite Boolean algebra>[finite-cofinite algebra] is a simple counterexample.
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