Journal of Symbolic Logic

Large cardinals and definable well-orders on the universe

Andrew D. Brooke-Taylor

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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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J. Symbolic Logic, Volume 74, Issue 2 (2009), 641-654.

First available in Project Euclid: 2 June 2009

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Brooke-Taylor, Andrew D. Large cardinals and definable well-orders on the universe. J. Symbolic Logic 74 (2009), no. 2, 641--654. doi:10.2178/jsl/1243948331.

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