2021
DOI: 10.4064/fm910-6-2020
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On the complexity of classes of uncountable structures: trees on $\aleph _1$

Abstract: We analyse the complexity of the class of (special) Aronszajn, Suslin and Kurepa trees in the projective hierarchy of the higher Baire space ω ω 1 1. First, we show that none of these classes have the Baire property (unless they are empty). Moreover, under V = L, (a) the class of Aronszajn and Suslin trees is Π 1 1-complete, (b) the class of special Aronszajn trees is Σ 1 1-complete, and (c) the class of Kurepa trees is Π 1 2-complete. We achieve these results by finding nicely definable reductions that map su… Show more

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