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arXiv · 1607.04904

On the consistency of local and global versions of Chang's Conjecture

Monroe Eskew·Yair Hayut
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Abstract

We show that for many pairs of infinite cardinals $\kappa > \mu^+ > \mu$, $(\kappa^{+}, \kappa)\twoheadrightarrow (\mu^+, \mu)$ is consistent relative to the consistency of a supercompact cardinal. We also show that it is consistent, relative to a huge cardinal that $(\kappa^{+}, \kappa)\twoheadrightarrow (\mu^+, \mu)$ for every successor cardinal $\kappa$ and every $\mu < \kappa$, answering a question of Foreman.

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Monroe Eskew, Yair Hayut. 2016-07-17. On the consistency of local and global versions of Chang's Conjecture. https://doi.org/10.1090/tran%2F7260

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