Boolean prime ideal theorem
= Boolean prime ideal theorem
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Every proper <lattice ideal> of a <Boolean algebra> extends to a prime <lattice ideal>. More generally, an ideal disjoint from a <lattice filter> extends to a prime ideal still disjoint from that filter. This Boolean case of the <Stone prime filter theorem> is equivalent to the <ultrafilter lemma> over <Zermelo–Fraenkel set theory> and is weaker than the <axiom of choice>.