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Hausdorff gaps and towers in $\mathcal {P}(\omega )/ {\rm Fin}$

Volume 229 / 2015

Piotr Borodulin-Nadzieja, David Chodounský Fundamenta Mathematicae 229 (2015), 197-229 MSC: 03E35, 03E05. DOI: 10.4064/fm229-3-1


We define and study two classes of uncountable $\subseteq ^*$-chains: Hausdorff towers and Suslin towers. We discuss their existence in various models of set theory. Some of the results and methods are used to provide examples of indestructible gaps not equivalent to a Hausdorff gap. We also indicate possible ways of developing a structure theory for towers based on classification of their Tukey types.


  • Piotr Borodulin-NadziejaInstytut Matematyczny
    Uniwersytet Wrocławski
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
  • David ChodounskýInstitute of Mathematics AS CR
    Žitná 25
    115 67 Praha 1, Czech Republic
    Department of Mathematics
    York University
    4700 Keele Street
    Toronto, Ontario M3J 1P3, Canada

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