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Successive failures of approachability

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Abstract

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 \(\left[ {{\aleph _2},{\aleph _{{\omega ^2} + 3}}} \right]\) and \({{\aleph _{{\omega ^2}}}}\) is strong limit.

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, 40 St. George St., Toronto, Ontario, M5S 2E4, Canada

    Spencer Unger

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  1. Spencer Unger
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Correspondence to Spencer Unger.

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Unger, S. Successive failures of approachability. Isr. J. Math. 242, 663–695 (2021). https://doi.org/10.1007/s11856-021-2138-9

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  • DOI: https://doi.org/10.1007/s11856-021-2138-9

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