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A proof of the independence of the axiom of choice from the Boolean prime ideal theorem. (English) Zbl 1363.03021
The Boolean prime ideal theorem states that ideals in Boolean algebras can always be extended to prime ideals. It was shown by J. D. Halpern and A. Levy [Proc. Sympos. Pure Math. 13, Part I, 83–134 (1971; Zbl 0233.02024)], that the Boolean prime ideal theorem does not imply the axiom of choice. The author gives a proof using a transitive model of ZF in which the axiom of choice does not hold. The original proof used the full Halpern-Läuchli partition theorem. Here the author presents a simplification by reducing the proof to its elementary case.

03E35 Consistency and independence results
03E25 Axiom of choice and related propositions
03E40 Other aspects of forcing and Boolean-valued models
03E45 Inner models, including constructibility, ordinal definability, and core models
Zbl 0233.02024
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