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arXiv · 1003.4707

Indestructibility of Vopenka's Principle

Andrew D. Brooke-Taylor
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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.

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Andrew D. Brooke-Taylor. 2010-03-24. Indestructibility of Vopenka's Principle. https://doi.org/10.1007/s00153-011-0228-9

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