Indestructibility of Vopěnka’s Principle

Andrew D Brooke-Taylor

Research output: Contribution to journalArticle (Academic Journal)peer-review

11 Citations (Scopus)


Vopenka's Principle is a natural large cardinal axiom that has recently found applications in category theory and algebraic topology. We show that
Vopenka's Principle and Vopenka cardinals are relatively consistent with a broad
range of other principles known to be independent of standard (ZFC) set theory,
such as the Generalised Continuum Hypothesis, and the existence of a denable
well-order on the universe of all sets. We achieve this by showing that they are indestructible under a broad class of forcing constructions, specically, reverse Easton
iterations of increasingly directed closed partial orders.
Original languageEnglish
Pages (from-to)515-529
Number of pages14
JournalArchive for Mathematical Logic
Issue number5-6
Publication statusPublished - 1 Jul 2011


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