Coding into HOD via normal measures with some applications |
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| Authors: | Arthur W Apter Shoshana Friedman |
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| Institution: | 1. Department of Mathematics, Baruch College of CUNY, New York, New York 10010, USA and the CUNY Graduate Center, Mathematics, 365 Fifth Avenue, New York, New York 10016, USA;2. Department of Mathematics and Computer Science, Kingsborough Community College‐CUNY, 2001 Oriental Boulevard, Brooklyn, New York 11235, USA |
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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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| Keywords: | Measurable cardinal supercompact cardinal normal measure HOD MSC (2010) 03E35 03E45 03E55 |
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