Miroslav Repický
A~proof of the independence of the Axiom of Choice from the Boolean Prime Ideal Theorem

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