The ground axiom.

Title: The ground axiom.
Identifier: AAI3231958
identifier: 3231958
Creator: Reitz, Jonas.
Contributor: Adviser: Joel David Hamkins
Date: 2006
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: A new axiom is proposed, the Ground Axiom, asserting that the universe is not a nontrivial set-forcing extension of any inner model. The Ground Axiom is first-order expressible, and any model of ZFC has a class-forcing extension which satisfies it. The Ground Axiom is independent of many well-known set-theoretic assertions including the Generalized Continuum Hypothesis, the assertion V=HOD that every set is ordinal definable, and the existence of measurable and supercompact cardinals. The related Bedrock Axiom, asserting that the universe is a set-forcing extension of a model satisfying the Ground Axiom, is also first-order expressible, and its negation is consistent. As many of these results rely on forcing with proper classes, an appendix is provided giving an exposition of the underlying theory of proper class forcing.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.