Journal of Symbolic Logic

Large cardinals and definable well-orders on the universe

Andrew D. Brooke-Taylor

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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 ♢*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.

Article information

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

Dates
First available in Project Euclid: 2 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1243948331

Digital Object Identifier
doi:10.2178/jsl/1243948331

Mathematical Reviews number (MathSciNet)
MR2518815

Zentralblatt MATH identifier
1166.03029

Citation

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. https://projecteuclid.org/euclid.jsl/1243948331


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