• A. W.~Apter and J. D. Hamkins, “Universal indestructibility,” Kobe Journal of Mathematics, vol. 16, iss. 2, p. 119–130, 1999.
  [Bibtex]

  @article {ApterHamkins99:UniversalIndestructibility,
  AUTHOR = {Arthur W.~Apter and Joel David Hamkins},
  TITLE = {Universal indestructibility},
  JOURNAL = {Kobe Journal of Mathematics},
  VOLUME = {16},
  YEAR = {1999},
  NUMBER = {2},
  PAGES = {119--130},
  ISSN = {0289-9051},
  MRCLASS = {03E55 (03E35)},
  MRNUMBER = {1745027 (2001k:03112)},
  MRNUMBER = {1 745 027},
  eprint = {math/9808004},
  archivePrefix = {arXiv},
  primaryClass = {math.LO},
  url = {http://wp.me/p5M0LV-12},
  }

From a suitable large cardinal hypothesis, we provide a model with a supercompact cardinal in which universal indestructibility holds: every supercompact and partially supercompact cardinal kappa is fully indestructible by kappa-directed closed forcing. Such a state of affairs is impossible with two supercompact cardinals or even with a cardinal which is supercompact beyond a measurable cardinal.