The tree property on a countable segment of successors of singular cardinals

TL;DR

This paper constructs a ZFC model demonstrating the tree property at a countable segment of successors of singular cardinals, starting from the assumption of many supercompact cardinals.

Contribution

It introduces a new method to establish the tree property at specific singular cardinal successors within a ZFC model.

Findings

Tree property holds at a countable segment of successors of singular cardinals

Model constructed from many supercompact cardinals

Advances understanding of combinatorial properties at singular cardinals

Abstract

Starting from the existence of many supercompact cardinals, we construct a model of ZFC in which the tree property holds at a countable segment of successor of singular cardinals.