The tree property at both $\aleph _{\omega +1}$ and $\aleph _{\omega +2}$
Volume 229 / 2015
Fundamenta Mathematicae 229 (2015), 83-100
MSC: Primary 03E05; Secondary 03E55.
DOI: 10.4064/fm229-1-3
Abstract
We force from large cardinals a model of ${\rm ZFC }$ in which $\aleph _{\omega +1}$ and $\aleph _{\omega +2}$ both have the tree property. We also prove that if we strengthen the large cardinal assumptions, then in the final model $\aleph _{\omega +2}$ even satisfies the super tree property.
