Abstract
Vopěnka’s Principle is a natural large cardinal axiom that has recently found applications in category theory and algebraic topology. We show that Vopěnka’s Principle and Vopěnka 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 definable well-order on the universe of all sets. We achieve this by showing that they are indestructible under a broad class of forcing constructions, specifically, reverse Easton iterations of increasingly directed closed partial orders.
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This research was conducted at the University of Bristol with support from the Heilbronn Institute for Mathematical Research.
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Brooke-Taylor, A.D. Indestructibility of Vopěnka’s Principle. Arch. Math. Logic 50, 515–529 (2011). https://doi.org/10.1007/s00153-011-0228-9
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DOI: https://doi.org/10.1007/s00153-011-0228-9
Keywords
- Forcing indestructibility
- Vopěnka’s Principle
- Vopěnka cardinals
- Reverse Easton iteration
- Master condition