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

Joel David Hamkins (The City University of New York); Mirna D\v{z}amonja (University of East Anglia)

arxiv: math/0409304 · v1 · submitted 2004-09-17 · 🧮 math.LO

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

Joel David Hamkins (The City University of New York) , Mirna D\v{z}amonja (University of East Anglia) This is my paper

classification 🧮 math.LO

keywords cardinalcardinalsdiamondkappastronglyunfoldablecompactcontinues

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If kappa is any strongly unfoldable cardinal, then this is preserved in a forcing extension in which Diamond_kappa(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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Diamond (on the regulars) can fail at any strongly unfoldable cardinal

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