Geodesic
On Todorcevic orderings
Bohuslav Balcar 1   ; Tomáš Pazák 2   ; Egbert Thümmel 3
1 Center 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
2 Institute of Information Theory and Automation of the ASCR Pod Vodárenskou věží 4 182 08 Praha 8, Czech Republic
3 Táborská 680/33 251 01 Říčany, Czech Republic
Fundamenta Mathematicae, Tome 228 (2015) no. 2, pp. 173-192 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm228-2-4
Keywords: todorcevic ordering mathbb consists finite families convergent sequences given topological space ordering defined special real line nbsp todorcevic example borel ordering satisfying ccc sigma finite even have knaster property interested properties mathbb where space taken parameter conditions given which ensure countable chain condition its stronger versions mathbb study properties mathbb forcing notion homogeneity generated complete boolean algebra

Bohuslav Balcar  1   ; Tomáš Pazák  2   ; Egbert Thümmel  3

1 Center 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
2 Institute of Information Theory and Automation of the ASCR Pod Vodárenskou věží 4 182 08 Praha 8, Czech Republic
3 Táborská 680/33 251 01 Říčany, Czech Republic 
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Bohuslav Balcar; Tomáš Pazák; Egbert Thümmel. On Todorcevic orderings. Fundamenta Mathematicae, Tome 228 (2015) no. 2, pp. 173-192. doi: 10.4064/fm228-2-4

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