Aronszajn tree

A κ-tree ( T for which |Tα|<κ for all α<κ and which has no cofinal branches is called a κ-Aronszajn tree. If κ=ω1 then it is referred to simply as an Aronszajn tree.

If there are no κ-Aronszajn trees for some κ then we say κ has the tree property. ω has the tree property, but no singular cardinal has the tree property.

Title Aronszajn tree
Canonical name AronszajnTree
Date of creation 2013-03-22 12:52:34
Last modified on 2013-03-22 12:52:34
Owner Henry (455)
Last modified by Henry (455)
Numerical id 10
Author Henry (455)
Entry type Definition
Classification msc 03E05
Classification msc 05C05
Related topic TreeSetTheoretic
Related topic AntichainMathworldPlanetmath
Related topic SuslinTree
Related topic WeaklyCompactCardinalsAndTheTreeProperty
Defines Aronszajn tree
Defines κ-Aronszajn tree
Defines tree property