Coding into HOD via normal measures with some applications

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.

• Type: Journal
• Year: 2011
• Where: MLQ
• Authors: Arthur W. Apter, Shoshana Friedman
• Keywords: Cardinal, Gch, Machine Learning, Measurable Cardinals, MLQ 2011