On Todorcevic orderings

• Autorzy: Bohuslav Balcar , Tomáš Pazák , Egbert Thümmel
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03E40: Other aspects of forcing and Boolean-valued models
• 03E05: Other combinatorial set theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 228
• Numer: 2
• Strony: 173-192

Daty

wydano

2015

Twórcy

autor

Bohuslav Balcar

• Center for Theoretical Study, Jilská 1, 110 00 Praha 1, Czech Republic
• Institute of Mathematics AS CR, Žitná 25, 115 67 Praha 1, Czech Republic

autor

Tomáš Pazák

• Institute of Information Theory and Automation of the ASCR, Pod Vodárenskou věží 4, 182 08 Praha 8, Czech Republic

autor

Egbert Thümmel

• Táborská 680/33, 251 01 Říčany, Czech Republic

Identyfikatory

DOI

10.4064/fm228-2-4