Inaccessible cardinals without the axiom of choice

Volume 194 / 2007

Andreas Blass, Ioanna M. Dimitriou, Benedikt Löwe Fundamenta Mathematicae 194 (2007), 179-189 MSC: Primary 03E10, 03E25; Secondary 03E55. DOI: 10.4064/fm194-2-3


We consider four notions of strong inaccessibility that are equivalent in $\mathsf {ZFC}$ and show that they are not equivalent in $\mathsf{ZF}$.


  • Andreas BlassDepartment of Mathematics
    University of Michigan
    Ann Arbor, MI 48109-1043, U.S.A.
  • Ioanna M. DimitriouMathematisches Institut
    Rheinische Friedrich-Wilhelms-Universität Bonn
    Beringstrasse 1
    53115 Bonn, Germany
  • Benedikt LöweInstitute for Logic,
    Language and Computation
    Universiteit van Amsterdam
    Plantage Muidergracht 24
    1018 TV Amsterdam, The Netherlands
    Department Mathematik
    Universität Hamburg
    Bundesstrasse 55
    20146 Hamburg, Germany

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