Strong tree properties for two successive cardinals

@article{Fontanella2012StrongTP,
  title={Strong tree properties for two successive cardinals},
  author={Laura Fontanella},
  journal={Archive for Mathematical Logic},
  year={2012},
  volume={51},
  pages={601-620}
}
  • Laura Fontanella
  • Published 31 October 2011
  • Mathematics
  • Archive for Mathematical Logic
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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