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

Itay Neeman; John Susice

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arXiv · 1810.03511

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

Itay Neeman·John Susice

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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 $\kappa$.

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BibTeX RIS

Itay Neeman, John Susice. 2018-10-08. Chang's Conjecture with $\square_{\omega_1, 2}$ from an $\omega_1$-Erd\H{o}s Cardinal. https://arxiv.org/abs/1810.03511

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