- 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.