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A characterization of the Boolean Prime Ideal theorem in terms of forcing notions

Volume 245 / 2019

David Fernández-Bretón, Elizabeth Lauri Fundamenta Mathematicae 245 (2019), 25-38 MSC: Primary 03E25; Secondary 03E65, 03E50, 03E57. DOI: 10.4064/fm558-5-2018 Published online: 7 January 2019


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.


  • David Fernández-BretónDepartment of Mathematics
    University of Michigan
    2074 East Hall
    530 Church Street
    Ann Arbor, MI 48109-1043, U.S.A.
    Kurt Gödel Research Center for Mathematical Logic
    University of Vienna
    Währinger Straße 25
    1090 Wien, Austria
  • Elizabeth LauriDepartment of Mathematics
    University of Connecticut
    341 Mansfield Road U1009
    Storrs, CT 06269-1009, U.S.A.
    Department of Mathematics
    Cornell University
    310 Malott Hall
    Ithaca, NY 14853, U.S.A.

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