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

@article{Golshani2015TheTP,
title={The tree property on a countable segment of successors of singular cardinals},
journal={arXiv: Logic},
year={2015}
}
• Published 9 December 2015
• Mathematics
• arXiv: Logic
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.
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Suppose that there is a huge cardinal. We prove that a two-stage iteration of Easton collapses produces a saturated filter on the successor of a regular cardinal.

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The model, where the two hold simultaneously, is another step toward the goal of obtaining the tree property on increasingly large intervals of successor cardinals.