Iterating along a Prikry sequence
Volume 232 / 2016
Fundamenta Mathematicae 232 (2016), 151-165
MSC: Primary 03E35; Secondary 03E55.
DOI: 10.4064/fm232-2-4
Abstract
We introduce a new method which combines Prikry forcing with an iteration between the Prikry points. Using our method we prove from large cardinals that it is consistent that the tree property holds at $\aleph _n$ for $n \geq 2$, $\aleph _\omega $ is strong limit and $2^{\aleph _\omega } = \aleph _{\omega +2}$.
