Diamond (on the regulars) can fail at any strongly unfoldable cardinal

[bibtex key=DzamonjaHamkins2006:DiamondCanFail]

If $\kappa$ is any strongly unfoldable cardinal, then this is preserved in a forcing extension in which $\Diamond_\kappa(\text{REG})$ fails. This result continues the progression of the corresponding results for weakly compact cardinals, due to Woodin, and for indescribable cardinals, due to Hauser.

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