Jech–Kunen tree

In mathematics, a ω₁-tree is a tree of power ω₁ and height ω₁. A Jech–Kunen tree is a ω₁-tree in which the number of branches is greater than ω₁ and less than 2^ω₁. It is named after Thomas Jech (1971) who found the first model in which this tree exists, and Kenneth Kunen (1975) who showed that, assuming the continuum hypothesis and 2^ω₁ > ω₂, the existence of a Jech–Kunen tree is equivalent to the existence of a compact Hausdorff space with weight ω₁ and cardinality strictly between ω₁ and 2^ω₁.

References

• Jech, Thomas J. (1971), "Trees", Journal of Symbolic Logic, 36: 1–14, doi:10.2307/2271510, MR 0284331
• Kunen (1975), "On the cardinality of compact spaces", Notices of the AMS, 22: 212
• Jin, Renling (1993), "The differences between Kurepa trees and Jech-Kunen trees", Archive for Mathematical Logic, 32: 369–379