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

2004/09/17 by Joel David Hamkins, Hamkins, Joel David, Mirna Džamonja +1
Mathematics · #03E05 #03E35 #03E55 #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03E05 #msc:03E35 #msc:03E55

paper · pdf · doi:10.48550/arxiv.math/0409304

25 pages

arxiv created 2004/09/17 · arxiv updated 2009/12/01

Abstract

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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