Consistency strengths of modified maximality principles.

Item

Title: Consistency strengths of modified maximality principles.
Identifier: AAI3144111
identifier: 3144111
Creator: Leibman, George.
Contributor: Adviser: Joel David Hamkins
Date: 2004
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: The Maximality Principle MP is a scheme which states that if a sentence of the language of ZFC is true in some forcing extension VP , and remains true in any further forcing extension of VP , then it is true in all forcing extensions of V. A modified maximality principle MPGamma arises when considering forcing with a particular class Gamma of forcing notions. A parametrized form of such a principle, MPGamma( X), considers formulas taking parameters; to avoid inconsistency such parameters must be restricted to a specific set X which depends on the forcing class Gamma being considered. A stronger necessary form of such a principle, &square;MP Gamma(X), occurs when it continues to be true in all Gamma forcing extensions.;This study uses iterated forcing, modal logic, and other techniques to establish consistency strengths for various modified maximality principles restricted to various forcing classes, including CCC, COHEN, COLL (the forcing notions that collapse ordinals to o), < kappa directed closed forcing notions, etc., both with and without parameter sets. Necessary forms of these principles are also considered.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.

Item sets: CUNY Legacy ETDs

Media: Consistency strengths of modified maximality principles.