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

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Abstract

If κ is any strongly unfoldable cardinal, then this is preserved in a forcing extension in which κ(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.

Keywords

Unfoldable cardinals
Infinite combinatorics
Diamond sequence
Laver function

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