• M. D{u{z}}amonja and J. D. Hamkins, “Diamond (on the regulars) can fail at any strongly unfoldable cardinal,” Ann.~Pure Appl.~Logic, vol. 144, iss. 1-3, p. 83–95, 2006.
  [Bibtex]

  @ARTICLE{DzamonjaHamkins2006:DiamondCanFail,
  AUTHOR = {D{\u{z}}amonja, Mirna and Hamkins, Joel David},
  TITLE = {Diamond (on the regulars) can fail at any strongly unfoldable cardinal},
  JOURNAL = {Ann.~Pure Appl.~Logic},
  FJOURNAL = {Annals of Pure and Applied Logic},
  VOLUME = {144},
  YEAR = {2006},
  NUMBER = {1-3},
  PAGES = {83--95},
  ISSN = {0168-0072},
  CODEN = {APALD7},
  MRCLASS = {03E05 (03E35 03E55)},
  MRNUMBER = {2279655 (2007m:03091)},
  MRREVIEWER = {Andrzej Ros{\l}anowski},
  DOI = {10.1016/j.apal.2006.05.001},
  URL = {http://jdh.hamkins.org/diamondcanfail/},
  month = {December},
  note = {Conference in honor of sixtieth birthday of James E.~Baumgartner},
  eprint = {math/0409304},
  archivePrefix = {arXiv},
  primaryClass = {math.LO},
  }

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.