Indestructibility of Vopenka's Principle
arXiv:1003.4707 · doi:10.1007/s00153-011-0228-9
Abstract
We show that Vopenka's Principle and Vopenka cardinals are indestructible under reverse Easton forcing iterations of increasingly directed-closed partial orders, without the need for any preparatory forcing. As a consequence, we are able to prove the relative consistency of these large cardinal axioms with a variety of statements known to be independent of ZFC, such as the generalised continuum hypothesis, the existence of a definable well-order of the universe, and the existence of morasses at many cardinals.
15 pages, submitted to Israel Journal of Mathematics