Strong tree Properties for two successive cardinals

Laura Fontanella

Strong tree Properties for two successive cardinals

Logic 2011-12-15 v5

Authors: Laura Fontanella

Abstract

An inaccessible cardinal $\kappa$ is supercompact when $(\kappa, \lambda)$ -ITP holds for all $\lambda\geq \kappa.$ 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 $\mu'\geq \aleph_3.$

Keywords

supercompact cardinal strong tree property ITP successive cardinals ZFC

Cite

@article{arxiv.1110.6736,
  title  = {Strong tree Properties for two successive cardinals},
  author = {Laura Fontanella},
  journal= {arXiv preprint arXiv:1110.6736},
  year   = {2011}
}

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