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Large cardinals and definable well-orders on the universe

Published online by Cambridge University Press:  12 March 2014

Andrew D. Brooke-Taylor
Andrew D. Brooke-Taylor*
Affiliation:
Department of Mathematics, University of Bristol, University Walk, Bristol, Bs8 1Tw, UK, E-mail: [email protected]
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 2 , June 2009 , pp. 641 - 654
Copyright
Copyright © Association for Symbolic Logic 2009

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