Chang's Conjecture with $\square_{\omega_1, 2}$ from an $\omega_1$-Erd\H{o}s Cardinal

Itay Neeman; John Susice

Chang's Conjecture with $\square_{\omega_1, 2}$ from an $\omega_1$-Erd\H{o}s Cardinal

Logic 2019-09-25 v4

Authors: Itay Neeman , John Susice

Abstract

Answering a question of Sakai, we show that the existence of an $\omega_1$ -Erd\H{o}s cardinal suffices to obtain the consistency of Chang's Conjecture with $\square_{\omega_1, 2}$ . By a result of Donder this is best possible. We also give an answer to another question of Sakai relating to the incompatibility of $\square_{\lambda, 2}$ and $(\lambda^+, \lambda) \twoheadrightarrow (\kappa^+, \kappa)$ for uncountable $\kappa$ .

Keywords

chang's conjecture erdős cardinal square principle consistency set theory large cardinals

Cite

@article{arxiv.1810.03511,
  title  = {Chang's Conjecture with $\square_{\omega_1, 2}$ from an $\omega_1$-Erd\H{o}s Cardinal},
  author = {Itay Neeman and John Susice},
  journal= {arXiv preprint arXiv:1810.03511},
  year   = {2019}
}

Chang's Conjecture with $\square_{\omega_1, 2}$ from an $\omega_1$-Erd\H{o}s Cardinal

Abstract

Keywords

Cite

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