A Cardinal Pattern Inspired by AD

Mathematical Logic Quarterly 42 (1):211-218 (1996)
  Copy   BIBTEX

Abstract

Assuming Con, a model in which there are unboundedly many regular cardinals below Θ and in which the only regular cardinals below Θ are limit cardinals was previously constructed. Using a large cardinal hypothesis far beyond Con, we construct in this paper a model in which there is a proper class of regular cardinals and in which the only regular cardinals in the universe are limit cardinals.

Categories

Keywords

Reprint years

DOI

10.1002/malq.19960420118

Other Versions

reprint Apter, Arthur W. (2006) "A Cardinal Pattern Inspired by AD". Mathematical Logic Quarterly 42(1):211-218

Links

PhilArchive

External links

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

Through your library

My notes

Similar books and articles

More on the Least Strongly Compact Cardinal.Arthur W. Apter - 1997 - Mathematical Logic Quarterly 43 (3):427-430.
Inner models with large cardinal features usually obtained by forcing.Arthur W. Apter, Victoria Gitman & Joel David Hamkins - 2012 - Archive for Mathematical Logic 51 (3-4):257-283.
Indestructibility, instances of strong compactness, and level by level inequivalence.Arthur W. Apter - 2010 - Archive for Mathematical Logic 49 (7-8):725-741.
Indestructible Weakly Compact Cardinals and the Necessity of Supercompactness for Certain Proof Schemata.Joel David Hamkins & Arthur W. Apter - 2001 - Mathematical Logic Quarterly 47 (4):563-572.
Removing Laver functions from supercompactness arguments.Arthur W. Apter - 2005 - Mathematical Logic Quarterly 51 (2):154.
Reducing the consistency strength of an indestructibility theorem.Arthur W. Apter - 2008 - Mathematical Logic Quarterly 54 (3):288-293.
Strong Compactness and a Global Version of a Theorem of Ben-David and Magidor.Arthur W. Apter - 2000 - Mathematical Logic Quarterly 46 (4):453-460.
Distributive proper forcing axiom and cardinal invariants.Huiling Zhu - 2013 - Archive for Mathematical Logic 52 (5-6):497-506.
Supercompactness and level by level equivalence are compatible with indestructibility for strong compactness.Arthur W. Apter - 2007 - Archive for Mathematical Logic 46 (3-4):155-163.
Making all cardinals almost Ramsey.Arthur W. Apter & Peter Koepke - 2008 - Archive for Mathematical Logic 47 (7-8):769-783.

Analytics

Added to PP
2013-12-01

Downloads
50 (#1,179,715)

6 months
6 (#1,502,802)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Making all cardinals almost Ramsey.Arthur W. Apter & Peter Koepke - 2008 - Archive for Mathematical Logic 47 (7-8):769-783.
How many normal measures can ℵ carry?Arthur W. Apter - 2010 - Mathematical Logic Quarterly 56 (2):164-170.

Add more citations

References found in this work

No references found.

Add more references