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Generic existence of ultrafilters on the natural numbers

Volume 236 / 2017

Jörg Brendle, Jana Flašková Fundamenta Mathematicae 236 (2017), 201-245 MSC: Primary 03E17; Secondary 03E15, 03E35, 03E50. DOI: 10.4064/fm730-5-2016 Published online: 24 November 2016


Say that a class of ultrafilters exists generically if every filter base of size $ \lt {\mathfrak c}$ can be extended to an ultrafilter in that class. We investigate generic existence of ultrafilters defined in terms of ideals on the natural numbers, like the summable ultrafilters and the density zero ultrafilters.


  • Jörg BrendleGraduate School of System Informatics
    Kobe University
    Rokko-dai 1-1, Nada-ku
    Kobe 657-8501, Japan
  • Jana FlaškováDepartment of Mathematics
    University of West Bohemia
    Univerzitní 22
    306 14 Plzeň, Czech Republic

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