# Large cardinals and definable well-orders on the universe

@article{BrookeTaylor2009LargeCA,
title={Large cardinals and definable well-orders on the universe},
author={Andrew D. Brooke-Taylor},
journal={The Journal of Symbolic Logic},
year={2009},
volume={74},
pages={641 - 654}
}
• A. Brooke-Taylor
• Published 16 November 2007
• Mathematics
• The Journal of Symbolic Logic
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 , 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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