The Todorcevic ordering 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 σ-finite cc and even need not have the Knaster property. We are interested in properties of 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 𝕋(X). We study the properties of 𝕋(X) as a forcing notion and the homogeneity of the generated complete Boolean algebra.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-2-4,
author = {Bohuslav Balcar and Tom\'a\v s Paz\'ak and Egbert Th\"ummel},
title = {On Todorcevic orderings},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {173-192},
zbl = {06390218},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-2-4}
}
Bohuslav Balcar; Tomáš Pazák; Egbert Thümmel. On Todorcevic orderings. Fundamenta Mathematicae, Tome 228 (2015) pp. 173-192. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-2-4/