Successive failures of approachability
classification
🧮 math.LO
keywords
alephapproachabilityaronszajnomegaspecialcannotcardinalcardinals
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Motivated by showing that in ZFC we cannot construct a special Aronszajn tree on some cardinal greater than $\aleph_1$, we produce a model in which the approachability property fails (hence there are no special Aronszajn trees) at all regular cardinals in the interval $[\aleph_2, \aleph_{\omega^2+3}]$ and $\aleph_{\omega^2}$ is strong limit.
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Forward citations
Cited by 1 Pith paper
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On the Intermediate Models of Strongly Compact Prikry Forcing
The authors characterize projections of strongly compact Prikry forcing using κ-complete fine measures, generalize prior results on κ-distributive forcings, and give Rudin-Keisler-style criteria for projections.
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