Square compactness and Lindel\"of trees
Logic
2023-05-26 v3
Abstract
We prove that every weakly square compact cardinal is a strong limit cardinal. We also study Aronszajn trees with no uncountable finitely branching subtrees, characterizing them in terms of being Lindel\"of with respect to a particular topology. We prove that the class of such trees lies between the classes of Suslin and Aronszajn trees, and that the inclusions can consistently be strict.
Cite
@article{arxiv.2301.08233,
title = {Square compactness and Lindel\"of trees},
author = {Pedro E. Marun},
journal= {arXiv preprint arXiv:2301.08233},
year = {2023}
}