The Tree Property up to $\aleph_{\omega^2}$

TL;DR

This paper constructs a model where the tree property holds at all regular cardinals from  to , extending previous results to a much larger range of cardinals.

Contribution

It demonstrates the consistency of the tree property at all regular cardinals up to , starting from a stationary set of supercompact cardinals.

Findings

Tree property holds at all regular cardinals between  and 

Uses a generic extension starting from supercompact cardinals

Extends known results to a broader range of cardinals.

Abstract

Starting from a stationary set of supercompact cardinals we find a generic extension in which the tree property holds at every regular cardinal between $\aleph_2$ and $\aleph_{\omega^2}$.