PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Borel Tukey morphisms and combinatorial cardinal invariants of the continuum

Volume 223 / 2013

Samuel Coskey, Tamás Mátrai, Juris Steprāns Fundamenta Mathematicae 223 (2013), 29-48 MSC: 03E15, 03E17. DOI: 10.4064/fm223-1-2


We discuss the Borel Tukey ordering on cardinal invariants of the continuum. We observe that this ordering makes sense for a larger class of cardinals than has previously been considered. We then provide a Borel version of a large portion of van Douwen's diagram. For instance, although the usual proof of the inequality ${\mathfrak {p}}\leq {\mathfrak {b}}$ does not provide a Borel Tukey map, we show that in fact there is one. Afterwards, we revisit a result of Mildenberger concerning a generalization of the unsplitting and splitting numbers. Lastly, we use our results to give an embedding from the inclusion ordering on $\mathcal P(\omega )$ into the Borel Tukey ordering on cardinal invariants.


  • Samuel CoskeyDepartment of Mathematics
    Boise State University
    1910 University Dr.
    Boise, ID 83725-1555, U.S.A.
    Formerly at York University
    Toronto, Canada
  • Tamás MátraiAlfréd Rényi Matematikai Kutatóintézet
    Magyar Tudományos Akadémia
    13-15 Reáltanoda utca
    H-1053 Budapest, Hungary
  • Juris SteprānsDepartment of Mathematics and Statistics, N520 Ross
    York University
    4700 Keele St.
    Toronto, ON, M3J 1P3, Canada

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image