Full Souslin trees at small cardinals

Assaf Rinot; Shira Yadai; Zhixing You

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arXiv · 2308.00299

Full Souslin trees at small cardinals

Assaf Rinot·Shira Yadai·Zhixing You

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Abstract

A $\kappa$-tree is said to be full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full $\kappa$-Souslin tree may consistently exist. Shelah gave an affirmative answer of height a strong limit Mahlo cardinal. Here, it is shown that these trees may consistently exist at small cardinals. Indeed, there can be $\aleph_3$ many full $\aleph_2$-trees such that the product of any countably many of them is an $\aleph_2$-Souslin tree.

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BibTeX RIS

Assaf Rinot, Shira Yadai, Zhixing You. 2023-08-01. Full Souslin trees at small cardinals. https://arxiv.org/abs/2308.00299

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