On Todorcevic orderings

Bohuslav Balcar, Tomáš Pazák, and Egbert Thümmel. "On Todorcevic orderings." Fundamenta Mathematicae 228.2 (2015): 173-192. <http://eudml.org/doc/286197>.

@article{BohuslavBalcar2015,
abstract = {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.},
author = {Bohuslav Balcar, Tomáš Pazák, Egbert Thümmel},
journal = {Fundamenta Mathematicae},
keywords = {partial ordering; ccc; forcing},
language = {eng},
number = {2},
pages = {173-192},
title = {On Todorcevic orderings},
url = {http://eudml.org/doc/286197},
volume = {228},
year = {2015},
}

TY - JOUR
AU - Bohuslav Balcar
AU - Tomáš Pazák
AU - Egbert Thümmel
TI - On Todorcevic orderings
JO - Fundamenta Mathematicae
PY - 2015
VL - 228
IS - 2
SP - 173
EP - 192
AB - 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.
LA - eng
KW - partial ordering; ccc; forcing
UR - http://eudml.org/doc/286197
ER -