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

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Monroe Eskew, Yair Hayut. 2019-09-06. On the consistency of local and global versions of Chang's Conjecture. https://doi.org/10.1090/tran%2F7260

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