Indestructibility of Vopenka's Principle

Details Indestructibility of Vopenka's Principle Indestructibility of Vopenka's Principle

2010-03-24

arxiv.org/abs/1003.4707v1

Archive for Mathematical Logic 50, no. 5 (2011) , pp 515-529

Mathematics

Logic

15 pages, submitted to Israel Journal of Mathematics

Scientific paper

10.1007/s00153-011-0228-9

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.

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