Definable Hamel bases and ${\sf AC}_\omega ({\mathbb R})$

Vladimir Kanovei, Ralf Schindler Fundamenta Mathematicae MSC: Primary 03E15; Secondary 03E35. DOI: 10.4064/fm909-6-2020 Published online: 17 December 2020


There is a model of ${\sf ZF}$ with a lightface $\Delta ^1_3$ definable Hamel bases in which ${\sf AC}_\omega ({\mathbb R})$ fails.


  • Vladimir KanoveiInstitute for the Information
    Transmission Problems
    Russian Academy of Sciences
    Bolshoy Karetny per. 19, build. 1
    Moscow 127051 Russia
  • Ralf SchindlerInstitut für Mathematische Logik
    und Grundlagenforschung
    Universität Münster
    48149 Münster, Germany

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