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Strong tree properties for small cardinals

Published online by Cambridge University Press:  12 March 2014

Laura Fontanella
Laura Fontanella*
Affiliation:
IMJ, Equipe de Logique Mathématique, Université Paris Diderot7, UFR de Mathematiques Case 7012, Site Chevaleret 75205, Paris Cedex 13, France, E-mail: fontanella@math.univ-paris-diderot.fr
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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 infinitely many supercompact cardinals, then there is a model of ZFC where for every n ≥ 2 and μ ≥ ℕn, we have (ℕn, μ)-ITP.

Keywords

tree propertylarge cardinalsforcing
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 1 , March 2013 , pp. 317 - 333
Copyright
Copyright © Association for Symbolic Logic 2013

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References

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