The tree property at successors of singular cardinals

&
Archive for Mathematical Logic 35 (5-6):385-404 (1996)
  Copy   BIBTEX

Abstract

Assuming some large cardinals, a model of ZFC is obtained in which $\aleph_{\omega+1}$ carries no Aronszajn trees. It is also shown that if $\lambda$ is a singular limit of strongly compact cardinals, then $\lambda^+$ carries no Aronszajn trees

Categories

Keywords

Reprint years

DOI

10.1007/s001530050052

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,100

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

Aronszajn trees and the successors of a singular cardinal.Spencer Unger - 2013 - Archive for Mathematical Logic 52 (5-6):483-496.
Review: Uri Abraham, Aronszajn Trees on $mathscr{N}2$ and $mathscr{N}3$; James Cummings, Matthew Foreman, The Tree Property; Menachem Magidor, Saharon Shelah, The Tree Property at Successors of Singular Cardinals. [REVIEW]Arthur W. Apter - 2001 - Bulletin of Symbolic Logic 7 (2):283-285.
Successors of singular cardinals and coloring theorems I.Todd Eisworth & Saharon Shelah - 2005 - Archive for Mathematical Logic 44 (5):597-618.
Some Problems in Singular Cardinals Combinatorics.Matthew Foreman - 2005 - Notre Dame Journal of Formal Logic 46 (3):309-322.
The tree property at [image].Dima Sinapova - 2012 - Journal of Symbolic Logic 77 (1):279 - 290.
On successors of Jónsson cardinals.J. Vickers & P. D. Welch - 2000 - Archive for Mathematical Logic 39 (6):465-473.
The tree property at ℵ ω+1.Dima Sinapova - 2012 - Journal of Symbolic Logic 77 (1):279-290.
Successors of Singular Cardinals and Coloring Theorems II.Todd Eisworth & Saharon Shelah - 2009 - Journal of Symbolic Logic 74 (4):1287 - 1309.
A remark on the tree property in a choiceless context.Arthur W. Apter - 2011 - Archive for Mathematical Logic 50 (5-6):585-590.
Making all cardinals almost Ramsey.Arthur W. Apter & Peter Koepke - 2008 - Archive for Mathematical Logic 47 (7-8):769-783.
The tree property and the failure of SCH at uncountable cofinality.Dima Sinapova - 2012 - Archive for Mathematical Logic 51 (5-6):553-562.
Strong tree properties for small cardinals.Laura Fontanella - 2013 - Journal of Symbolic Logic 78 (1):317-333.
Souslin trees and successors of singular cardinals.Shai Ben-David & Saharon Shelah - 1986 - Annals of Pure and Applied Logic 30 (3):207-217.
On the free subset property at singular cardinals.Peter Koepke - 1989 - Archive for Mathematical Logic 28 (1):43-55.

Analytics

Added to PP
2013-11-23

Downloads
61 (#264,627)

6 months
9 (#312,765)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Squares, scales and stationary reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
Aronszajn trees and failure of the singular cardinal hypothesis.Itay Neeman - 2009 - Journal of Mathematical Logic 9 (1):139-157.
The tree property up to אω+1.Itay Neeman - 2014 - Journal of Symbolic Logic 79 (2):429-459.
Aronszajn trees and the successors of a singular cardinal.Spencer Unger - 2013 - Archive for Mathematical Logic 52 (5-6):483-496.
Fragility and indestructibility of the tree property.Spencer Unger - 2012 - Archive for Mathematical Logic 51 (5-6):635-645.

View all 36 citations / Add more citations

References found in this work

Set Theory.T. Jech - 2005 - Bulletin of Symbolic Logic 11 (2):243-245.
The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.

Add more references