KnowraBoolean prime ideal theoremLinked fromLinked fromThe 4 pages that link to Boolean prime ideal theorem, each with the reason it gives.All 4Related 2Compared with 2Compactness theoremRelated: In set theory, this choice principle is equivalent to compactness for first-order logic.Axiom of countable choiceCompared with: It is weaker than full choice, offering a useful comparison among set-theoretic choice principles.Krull's theoremCompared with: It is a weaker choice principle related to maximal ideals in Boolean algebras, not the full ring theorem.Lindenbaum's lemmaRelated: Its algebraic extension principle parallels Lindenbaum extension and generalizes it beyond countable constructions.