Aronszajn and Kurepa trees
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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.
KeywordsAronszajn tree Kurepa tree Mitchell forcing Forcing axioms
Mathematics Subject Classification03E35
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