Abstract: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-L\"auchli partition theorem and instead we reduce the proof to its elementary case.
Keywords: Boolean Prime Ideal Theorem; the Axiom of Choice
DOI: DOI 10.14712/1213-7243.2015.138
AMS Subject Classification: 03E35 03E25 03E40 03E45