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On Todorcevic orderings

Volume 228 / 2015

Bohuslav Balcar, Tomáš Pazák, Egbert Thümmel Fundamenta Mathematicae 228 (2015), 173-192 MSC: Primary 03E05; Secondary 03E40. DOI: 10.4064/fm228-2-4

Abstract

The Todorcevic ordering $\mathbb {T}(X)$ consists of all finite families of convergent sequences in a given topological space $X$. Such an ordering was defined for the special case of the real line by S. Todorcevic (1991) as an example of a Borel ordering satisfying ccc that is not $\sigma $-finite cc and even need not have the Knaster property. We are interested in properties of $\mathbb {T}(X)$ where the space $X$ is taken as a parameter. Conditions on $X$ are given which ensure the countable chain condition and its stronger versions for $\mathbb {T}(X)$. We study the properties of $\mathbb {T}(X)$ as a forcing notion and the homogeneity of the generated complete Boolean algebra.

Authors

  • Bohuslav BalcarCenter for Theoretical Study
    Jilská 1
    110 00 Praha 1, Czech Republic
    and
    Institute of Mathematics AS CR
    Žitná 25
    115 67 Praha 1, Czech Republic
    e-mail
  • Tomáš PazákInstitute of Information Theory
    and Automation of the ASCR
    Pod Vodárenskou věží 4
    182 08 Praha 8, Czech Republic
    e-mail
  • Egbert ThümmelTáborská 680/33
    251 01 Říčany, Czech Republic
    e-mail

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