Some structural results concerning supercompact cardinals

Journal of Symbolic Logic 66 (4):1919-1927 (2001)
  Copy   BIBTEX

Abstract

We show how the forcing of [5] can be iterated so as to get a model containing supercompact cardinals in which every measurable cardinal δ is δ + supercompact. We then apply this iteration to prove three additional theorems concerning the structure of the class of supercompact cardinals

Categories

Keywords

Reprint years

DOI

10.2307/2694985

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,168

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

Large cardinals and large dilators.Andy Lewis - 1998 - Journal of Symbolic Logic 63 (4):1496-1510.
On measurable limits of compact cardinals.Arthur W. Apter - 1999 - Journal of Symbolic Logic 64 (4):1675-1688.
Gap forcing: Generalizing the lévy-Solovay theorem.Joel David Hamkins - 1999 - Bulletin of Symbolic Logic 5 (2):264-272.
The least measurable can be strongly compact and indestructible.Arthur W. Apter & Moti Gitik - 1998 - Journal of Symbolic Logic 63 (4):1404-1412.
Forcing axioms, supercompact cardinals, singular cardinal combinatorics.Matteo Viale - 2008 - Bulletin of Symbolic Logic 14 (1):99-113.
Identity crises and strong compactness.Arthur W. Apter & James Cummings - 2000 - Journal of Symbolic Logic 65 (4):1895-1910.
On a combinatorial property of Menas related to the partition property for measures on supercompact cardinals.Kenneth Kunen & Donald H. Pelletier - 1983 - Journal of Symbolic Logic 48 (2):475-481.
Abstract logic and set theory. II. large cardinals.Jouko Väänänen - 1982 - Journal of Symbolic Logic 47 (2):335-346.
Exactly controlling the non-supercompact strongly compact cardinals.Arthur W. Apter & Joel David Hamkins - 2003 - Journal of Symbolic Logic 68 (2):669-688.

Analytics

Added to PP
2009-01-28

Downloads
51 (#313,426)

6 months
27 (#111,271)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Failures of SCH and Level by Level Equivalence.Arthur W. Apter - 2006 - Archive for Mathematical Logic 45 (7):831-838.
Inaccessible Cardinals, Failures of GCH, and Level-by-Level Equivalence.Arthur W. Apter - 2014 - Notre Dame Journal of Formal Logic 55 (4):431-444.

Add more citations

References found in this work

On strong compactness and supercompactness.Telis K. Menas - 1975 - Annals of Mathematical Logic 7 (4):327-359.
Gap forcing: Generalizing the lévy-Solovay theorem.Joel David Hamkins - 1999 - Bulletin of Symbolic Logic 5 (2):264-272.
Destruction or preservation as you like it.Joel David Hamkins - 1998 - Annals of Pure and Applied Logic 91 (2-3):191-229.
Patterns of compact cardinals.Arthur W. Apter - 1997 - Annals of Pure and Applied Logic 89 (2-3):101-115.

Add more references