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The tree property at both $\aleph _{\omega +1}$ and $\aleph _{\omega +2}$

Volume 229 / 2015

Laura Fontanella, Sy David Friedman Fundamenta Mathematicae 229 (2015), 83-100 MSC: Primary 03E05; Secondary 03E55. DOI: 10.4064/fm229-1-3

Abstract

We force from large cardinals a model of ${\rm ZFC }$ in which $\aleph _{\omega +1}$ and $\aleph _{\omega +2}$ both have the tree property. We also prove that if we strengthen the large cardinal assumptions, then in the final model $\aleph _{\omega +2}$ even satisfies the super tree property.

Authors

  • Laura FontanellaKurt Gödel Research Center for Mathematical Logic
    University of Vienna
    1090 Wien, Austria
    e-mail
  • Sy David FriedmanKurt Gödel Research Center for Mathematical Logic
    University of Vienna
    1090 Wien, Austria
    e-mail

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