On a class of maximality principles

Archive for Mathematical Logic 57 (5-6):713-725 (2018)
  Copy   BIBTEX

Abstract

We study various classes of maximality principles, \\), introduced by Hamkins :527–550, 2003), where \ defines a class of forcing posets and \ is an infinite cardinal. We explore the consistency strength and the relationship of \\) with various forcing axioms when \. In particular, we give a characterization of bounded forcing axioms for a class of forcings \ in terms of maximality principles MP\\) for \ formulas. A significant part of the paper is devoted to studying the principle MP\\) where \ and \ defines the class of stationary set preserving forcings. We show that MP\\) has high consistency strength; on the other hand, if \ defines the class of proper forcings or semi-proper forcings, then by Hamkins, MP\\) is consistent relative to \.

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 103,566

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Absoluteness via resurrection.Giorgio Audrito & Matteo Viale - 2017 - Journal of Mathematical Logic 17 (2):1750005.
Closed Maximality Principles and Generalized Baire Spaces.Philipp Lücke - 2019 - Notre Dame Journal of Formal Logic 60 (2):253-282.
Class Forcing in Class Theory.Carolin Antos - 2018 - In Carolin Antos, Sy-David Friedman, Radek Honzik & Claudio Ternullo, The Hyperuniverse Project and Maximality. Basel, Switzerland: Birkhäuser. pp. 1-16.
Combined Maximality Principles up to large cardinals.Gunter Fuchs - 2009 - Journal of Symbolic Logic 74 (3):1015-1046.
A maximal bounded forcing axiom.David Asperó - 2002 - Journal of Symbolic Logic 67 (1):130-142.
A Lifting Argument for the Generalized Grigorieff Forcing.Radek Honzík & Jonathan Verner - 2016 - Notre Dame Journal of Formal Logic 57 (2):221-231.
The Consistency Strength of M P C C C.George Leibman - 2010 - Notre Dame Journal of Formal Logic 51 (2):181-193.

Analytics

Added to PP
2017-11-28

Downloads
39 (#619,836)

6 months
9 (#381,277)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Combining resurrection and maximality.Kaethe Minden - 2021 - Journal of Symbolic Logic 86 (1):397-414.

Add more citations

References found in this work

Set-theoretic geology.Gunter Fuchs, Joel David Hamkins & Jonas Reitz - 2015 - Annals of Pure and Applied Logic 166 (4):464-501.
Bounded forcing axioms as principles of generic absoluteness.Joan Bagaria - 2000 - Archive for Mathematical Logic 39 (6):393-401.
Set mapping reflection.Justin Tatch Moore - 2005 - Journal of Mathematical Logic 5 (1):87-97.
A simple maximality principle.Joel Hamkins - 2003 - Journal of Symbolic Logic 68 (2):527-550.
Resurrection axioms and uplifting cardinals.Joel David Hamkins & Thomas A. Johnstone - 2014 - Archive for Mathematical Logic 53 (3-4):463-485.

View all 11 references / Add more references