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

Eskew, Monroe; Hayut, Yair

doi:10.1090/tran/7260

On the consistency of local and global versions of Chang’s Conjecture
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by Monroe Eskew and Yair Hayut PDF

Trans. Amer. Math. Soc. 370 (2018), 2879-2905 Request permission

Corrigendum: Trans. Amer. Math. Soc. 374 (2021), 753-753.

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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