A Characterization of the Boolean Prime Ideal Theorem in Terms of Forcing Notions
Logic
2019-03-27 v2
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.
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Cite
@article{arxiv.1609.02630,
title = {A Characterization of the Boolean Prime Ideal Theorem in Terms of Forcing Notions},
author = {David Fernández-Bretón and Elizabeth Lauri},
journal= {arXiv preprint arXiv:1609.02630},
year = {2019}
}
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12 Pages