Strongly unfoldable cardinals made indestructible.

Title: Strongly unfoldable cardinals made indestructible.
Identifier: AAI3283167
identifier: 3283167
Creator: Johnstone, Thomas A.
Contributor: Adviser: Joel David Hamkins
Date: 2007
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: I provide indestructibility results for weakly compact, indescribable and strongly unfoldable cardinals. In order to make these large cardinals indestructible, I assume the existence of a strongly unfoldable cardinal kappa, which is a hypothesis consistent with V = L. The main result shows that any strongly unfoldable cardinal kappa can be made indestructible by all <kappa-closed forcing which does not collapse kappa+. As strongly unfoldable cardinals strengthen both indescribable and weakly compact cardinals, I obtain indestructibility for these cardinals also, thereby reducing the large cardinal hypothesis of previously known indestructibility results for these cardinals significantly. Finally, I use the developed methods to show the consistency of a weakening of the Proper Forcing Axiom PFA relative to the existence of a strongly unfoldable cardinal.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.