Aspects of supercompactness, HOD and set theoretic geology

Title: Aspects of supercompactness, HOD and set theoretic geology
Identifier: d_2009_2013:6da408657d1a:10166
identifier: 10347
Creator: Friedman, Shoshana,
Contributor: Arthur W. Apter
Date: 2009
Language: English
Publisher: City University of New York.
Subject: Mathematics | forcing and large cardinals | HOD | set theory | supercompact cardinals
Abstract: In this thesis, we study HOD, primarily in the context of large cardinals and GCH. Chapter 1 contains our introductory comments and preliminary remarks. In Chapter 2, we extend a property of HOD-supercompactness due to Sargsyan to various models of set theory containing supercompact cardinals. In doing so, we develop a new method for coding sets while preserving GCH. In Chapter 3, we extend this alternative method of coding. This allows us to produce models of V = HOD and GCH in the presence of large cardinals (including supercompact cardinals). In the remaining chapters, we use this coding to extend a variety of earlier results. In Chapter 4, we generalize theorems about the Ground Axiom to models with supercompact cardinals that satisfy GCH. In Chapter 5, we extend results in set theoretic geology to models that satisfy GCH. Finally, in Chapter 6, we use the coding to produce a model of the Wholeness Axiom, V = HOD and GCH.
Type: dissertation
Source: 2009_2013.csv
degree: Ph.D.
Program: Mathematics