Coding into HOD via normal measures with some applications

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

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10.1002/malq.201010010

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Citations of this work

Indestructibility, HOD, and the Ground Axiom.Arthur W. Apter - 2011 - Mathematical Logic Quarterly 57 (3):261-265.
Accessing the switchboard via set forcing.Shoshana Friedman - 2012 - Mathematical Logic Quarterly 58 (4-5):303-306.

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References found in this work

Elementary embeddings and infinitary combinatorics.Kenneth Kunen - 1971 - Journal of Symbolic Logic 36 (3):407-413.
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.

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