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Quadruples and cubes
We prove, in $\mathsf{ZFC}$, that the $λ$-terraced cube relation fails whenever $λ$ is an uncountable cardinal. The corresponding terraced relation for quadruples fails for every $λ$. If $λ$ is $\aleph_0$ then the pretinent terraced relation has consistency strength of at least one Woodin cardinal.
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