Abstract
Monroe Eskew (Tree properties on \(\omega _1\) and \(\omega _2\), 2016. https://mathoverflow.net/questions/217951/tree-properties-on-omega-1-and-omega-2) asked whether the tree property at \(\omega _2\) implies there is no Kurepa tree (as is the case in the Mitchell model, or under PFA). We prove that the tree property at \(\omega _2\) is consistent with the existence of \(\omega _1\)-trees with as many branches as desired.
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This work was partially supported by National Science Foundation grant DMS-1500790. I would like to thank the School of Mathematics at the IPM in Tehran for their warm hospitality in October 2015, with special thanks to Mohammad Golshani for many interesting conversations.
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Cummings, J. Aronszajn and Kurepa trees. Arch. Math. Logic 57, 83–90 (2018). https://doi.org/10.1007/s00153-017-0579-y
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DOI: https://doi.org/10.1007/s00153-017-0579-y