The tree property at $\aleph _{\omega +2}$ with a finite gap
Volume 251 / 2020
Fundamenta Mathematicae 251 (2020), 219-244
MSC: Primary 03E35; Secondary 03E55.
DOI: 10.4064/fm866-2-2020
Published online: 19 June 2020
Abstract
Let $n$ be a natural number, $2 \le n \lt \omega $. We show that it is consistent to have a model of set theory where $\aleph _\omega $ is strong limit, $2^{\aleph _\omega } = \aleph _{\omega +n}$, and the tree property holds at $\aleph _{\omega +2}$; we use a hypermeasurable cardinal of an appropriate degree and a variant of the Mitchell forcing followed by the Prikry forcing with collapses.
