arXiv 1003.47072010-03-24math.LO

Indestructibility of Vopenka's Principle

Andrew D. Brooke-Taylor

备注：: 15 pages, submitted to Israel Journal of Mathematics
发表信息：: Archive for Mathematical Logic 50, no. 5 (2011) , pp 515-529
DOI：: 10.1007/s00153-011-0228-9

英文摘要：

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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