Diamond, square, and level by level equivalence

Archive for Mathematical Logic 44 (3):387-395 (2005)
  Copy   BIBTEX

Abstract

We force and construct a model in which level by level equivalence between strong compactness and supercompactness holds, along with certain additional combinatorial properties. In particular, in this model, ♦ δ holds for every regular uncountable cardinal δ, and below the least supercompact cardinal κ, □ δ holds on a stationary subset of κ. There are no restrictions in our model on the structure of the class of supercompact cardinals

Categories

Keywords

Reprint years

DOI

10.1007/s00153-004-0252-0

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,386

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

An L-like model containing very large cardinals.Arthur W. Apter & James Cummings - 2008 - Archive for Mathematical Logic 47 (1):65-78.
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.
Failures of SCH and Level by Level Equivalence.Arthur W. Apter - 2006 - Archive for Mathematical Logic 45 (7):831-838.
Tallness and level by level equivalence and inequivalence.Arthur W. Apter - 2010 - Mathematical Logic Quarterly 56 (1):4-12.
Failure of GCH and the level by level equivalence between strong compactness and supercompactness.Arthur W. Apter - 2003 - Mathematical Logic Quarterly 49 (6):587.
Level by level inequivalence beyond measurability.Arthur W. Apter - 2011 - Archive for Mathematical Logic 50 (7-8):707-712.
Supercompactness and measurable limits of strong cardinals II: Applications to level by level equivalence.Arthur W. Apter - 2006 - Mathematical Logic Quarterly 52 (5):457-463.
Level by level equivalence and strong compactness.Arthur W. Apter - 2004 - Mathematical Logic Quarterly 50 (1):51.
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.
Indestructibility and level by level equivalence and inequivalence.Arthur W. Apter - 2007 - Mathematical Logic Quarterly 53 (1):78-85.
An Easton theorem for level by level equivalence.Arthur W. Apter - 2005 - Mathematical Logic Quarterly 51 (3):247-253.
Indestructible strong compactness and level by level inequivalence.Arthur W. Apter - 2013 - Mathematical Logic Quarterly 59 (4-5):371-377.
Indestructibility and the level-by-level agreement between strong compactness and supercompactness.Arthur W. Apter & Joel David Hamkins - 2002 - Journal of Symbolic Logic 67 (2):820-840.

Analytics

Added to PP
2013-11-23

Downloads
28 (#555,203)

6 months
7 (#411,886)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Strong Compactness, Square, Gch, and Woodin Cardinals.Arthur W. Apter - forthcoming - Journal of Symbolic Logic:1-9.
An L-like model containing very large cardinals.Arthur W. Apter & James Cummings - 2008 - Archive for Mathematical Logic 47 (1):65-78.

Add more citations

References found in this work

Strong axioms of infinity and elementary embeddings.Robert M. Solovay - 1978 - Annals of Mathematical Logic 13 (1):73.
Squares, scales and stationary reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
[Omnibus Review].Akihiro Kanamori - 1981 - Journal of Symbolic Logic 46 (4):864-866.
On strong compactness and supercompactness.Telis K. Menas - 1975 - Annals of Mathematical Logic 7 (4):327-359.

View all 11 references / Add more references