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Strong tree properties for two successive cardinals

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Abstract

An inaccessible cardinal κ is supercompact when (κ, λ)-ITP holds for all λ ≥ κ. We prove that if there is a model of ZFC with two supercompact cardinals, then there is a model of ZFC where simultaneously \({(\aleph_2, \mu)}\) -ITP and \({(\aleph_3, \mu')}\) -ITP hold, for all \({\mu\geq \aleph_2}\) and \({\mu'\geq \aleph_3}\) .

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  1. CNRS, IMJ, UMR 7586, Univ Paris Diderot, Sorbonne Paris Cité, 75205, Paris, France

    Laura Fontanella

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  1. Laura Fontanella
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Correspondence to Laura Fontanella.

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Fontanella, L. Strong tree properties for two successive cardinals. Arch. Math. Logic 51, 601–620 (2012). https://doi.org/10.1007/s00153-012-0285-8

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  • DOI: https://doi.org/10.1007/s00153-012-0285-8

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