A characterization of the Boolean Prime Ideal theorem in terms of forcing notions
Volume 245 / 2019
Fundamenta Mathematicae 245 (2019), 25-38
MSC: Primary 03E25; Secondary 03E65, 03E50, 03E57.
DOI: 10.4064/fm558-5-2018
Published online: 7 January 2019
Abstract
For certain weak versions of the Axiom of Choice (most notably, the Boolean Prime Ideal theorem), we obtain equivalent formulations in terms of partial orders, and filter-like objects within them intersecting certain dense sets or antichains. This allows us to prove some consequences of the Boolean Prime Ideal theorem using arguments in the style of those that use Zorn’s Lemma or Martin’s Axiom.
