Coding into HOD via normal measures with some applications

Mathematical Logic Quarterly 57 (4):366-372 (2011)

Abstract
We develop a new method for coding sets while preserving GCH in the presence of large cardinals, particularly supercompact cardinals. We will use the number of normal measures carried by a measurable cardinal as an oracle, and therefore, in order to code a subset A of κ, we require that our model contain κ many measurable cardinals above κ. Additionally we will describe some of the applications of this result. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Keywords supercompact cardinal  03E55  normal measure  Measurable cardinal  03E45  MSC (2010) 03E35  HOD
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DOI 10.1002/malq.201010010
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References found in this work BETA

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 Ground Axiom.Jonas Reitz - 2007 - Journal of Symbolic Logic 72 (4):1299 - 1317.
Elementary Embeddings and Infinitary Combinatorics.Kenneth Kunen - 1971 - Journal of Symbolic Logic 36 (3):407-413.

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Citations of this work BETA

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