## Miroslav Repický

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

Comment.Math.Univ.Carolin. 56,4 (2015) 543-546.**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

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