### A proof of the independence of the Axiom of Choice from the Boolean Prime Ideal Theorem

Miroslav Repický (2015)

Commentationes Mathematicae Universitatis Carolinae

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We present a proof of the Boolean Prime Ideal Theorem in a transitive model of ZF in which the Axiom of Choice does not hold. We omit the argument based on the full Halpern-Läuchli partition theorem and instead we reduce the proof to its elementary case.