A countable dense homogeneous set of reals of size $\aleph_1$

Volume 186 / 2005

Ilijas Farah, Michael Hrušák, Carlos Azarel Martínez Ranero Fundamenta Mathematicae 186 (2005), 71-77 MSC: 54E52, 54H05, 03E15. DOI: 10.4064/fm186-1-5

Abstract

We prove there is a countable dense homogeneous subspace of $\Bbb R$ of size~$\aleph_1$. The proof involves an absoluteness argument using an extension of the $L_{\omega_1\omega}(Q)$ logic obtained by adding predicates for Borel sets.

Authors

  • Ilijas FarahDepartment of Mathematics and Statistics
    York University
    4700 Keele Street
    Toronto, Canada M3J 1P3
    and
    Matematicki Institut
    Kneza Mihaila 35
    11000 Beograd
    Serbia and Montenegro
    e-mail
  • Michael HrušákInstituto de Matemáticas
    UNAM
    Unidad Morelia, A.P. 61-3
    Xangari, C.P. 58089
    Morelia, Mich., México
    e-mail
  • Carlos Azarel Martínez RaneroInstituto de Matemáticas
    UNAM
    Unidad Morelia, A.P. 61-3
    Xangari, C.P. 58089
    Morelia, Mich., México
    e-mail

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