Large cardinals and definable well-orders on the universe

Journal of Symbolic Logic 74 (2):641-654 (2009)

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 ◊ $_{k^ - }^* $ at a proper class of cardinals k. 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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DOI 10.2178/jsl/1243948331
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References found in this work BETA

Squares, Scales and Stationary Reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
The Lottery Preparation.Joel David Hamkins - 2000 - Annals of Pure and Applied Logic 101 (2-3):103-146.
Gap Forcing: Generalizing the Lévy-Solovay Theorem.Joel David Hamkins - 1999 - Bulletin of Symbolic Logic 5 (2):264-272.
The Wholeness Axioms and V=HOD.Joel David Hamkins - 2001 - Archive for Mathematical Logic 40 (1):1-8.

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