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June 2009 Large cardinals and definable well-orders on the universe
Andrew D. Brooke-Taylor
J. Symbolic Logic 74(2): 641-654 (June 2009). DOI: 10.2178/jsl/1243948331

Abstract

We use a reverse Easton forcing iteration to obtain a universe with a definable well-order, while preserving the GCH and proper classes of a variety of very large cardinals. This is achieved by coding using the principle ♢*κ+ at a proper class of cardinals κ. By choosing the cardinals at which coding occurs sufficiently sparsely, we are able to lift the embeddings witnessing the large cardinal properties without having to meet any non-trivial master conditions.

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Andrew D. Brooke-Taylor. "Large cardinals and definable well-orders on the universe." J. Symbolic Logic 74 (2) 641 - 654, June 2009. https://doi.org/10.2178/jsl/1243948331

Information

Published: June 2009
First available in Project Euclid: 2 June 2009

zbMATH: 1166.03029
MathSciNet: MR2518815
Digital Object Identifier: 10.2178/jsl/1243948331

Rights: Copyright © 2009 Association for Symbolic Logic

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Vol.74 • No. 2 • June 2009
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