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Indestructibility of Vopěnka’s Principle

Indestructibility of Vopěnka’s Principle 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

Indestructibility of Vopěnka’s Principle

Archive for Mathematical Logic , Volume 50 (6) – Jan 28, 2011

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References (45)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer-Verlag
Subject
Mathematics; Mathematics, general; Algebra; Mathematical Logic and Foundations
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/s00153-011-0228-9
Publisher site
See Article on Publisher Site

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.

Journal

Archive for Mathematical LogicSpringer Journals

Published: Jan 28, 2011

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