A note on the eightfold way

Gilton, Thomas; Krueger, John

doi:10.1090/proc/14771

A note on the eightfold way
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by Thomas Gilton and John Krueger PDF

Proc. Amer. Math. Soc. 148 (2020), 1283-1293 Request permission

Abstract:

Assuming the existence of a Mahlo cardinal, we construct a model in which there exists an $\omega _2$-Aronszajn tree, the $\omega _1$-approachability property fails, and every stationary subset of $\omega _2 \cap \text {cof}(\omega )$ reflects. This solves an open problem of Cummings et al. [J. Symb. Log. 83 (2018), no. 1, pp. 349–371]

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