- 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, pp. 83-95, 2006. (Conference in honor of sixtieth birthday of James E.~Baumgartner)
`@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 = {}, 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.