Hostname: page-component-6766d58669-fx4k7 Total loading time: 0 Render date: 2026-05-21T12:46:50.505Z Has data issue: false hasContentIssue false
  • English
  • Français

DESTRUCTIBILITY OF THE TREE PROPERTY AT ${\aleph _{\omega + 1}}$

Published online by Cambridge University Press:  06 March 2019

YAIR HAYUT  and
MENACHEM MAGIDOR
YAIR HAYUT
Affiliation:
EINSTEIN INSTITUTE OF MATHEMATICS EDMOND J. SAFRA CAMPUS, THE HEBREW UNIVERSITY OF JERUSALEM GIVAT RAM. JERUSALEM, 9190401, ISRAELE-mail: yair.hayut@mail.huji.ac.il
MENACHEM MAGIDOR
Affiliation:
EINSTEIN INSTITUTE OF MATHEMATICS EDMOND J. SAFRA CAMPUS, THE HEBREW UNIVERSITY OF JERUSALEM GIVAT RAM. JERUSALEM, 9190401, ISRAELE-mail: mensara@savion.huji.ac.il
Get access Rights & Permissions [Opens in a new window]

Abstract

We construct a model in which the tree property holds in ${\aleph _{\omega + 1}}$ and it is destructible under $Col\left( {\omega ,{\omega _1}} \right)$. On the other hand we discuss some cases in which the tree property is indestructible under small or closed forcings.

Keywords

03E3503E55tree propertysuccessors of singularsforcing

Information

Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 2 , June 2019 , pp. 621 - 631
Copyright
Copyright © The Association for Symbolic Logic 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Ben-David, S. and Shelah, S., Souslin trees and successors of singular cardinals. Annals of Pure and Applied Logic, vol. 30 (1986), no. 3, pp. 207–217.CrossRefGoogle Scholar
Cummings, J., Foreman, M., and Magidor, M., Squares, scales and stationary reflection. Journal of Mathematical Logic, vol. 1 (2001), no. 1, pp. 35–98.CrossRefGoogle Scholar
Lambie-Hanson, C., Squares and narrow systems, this Journal, vol. 82 (2017), no. 3, pp. 834–859.Google Scholar
Magidor, M. and Shelah, S., The tree property at successors of singular cardinals. Archive for Mathematical Logic, vol. 35 (1996), no. 5–6, pp. 385–404.CrossRefGoogle Scholar
Neeman, I., The tree property up to ${\aleph _{\omega + 1}}$, this Journal, vol. 79 (2014), no. 2, pp. 429–459.Google Scholar
Rinot, A., A cofinality-preserving small forcing may introduce a special Aronszajn tree, Archive for Mathematical Logic. vol. 48 (2009), no. 8, pp. 817–823.CrossRefGoogle Scholar
Sinapova, D., The tree property and the failure of the singular cardinal hypothesis at ${\aleph _{{\omega ^2}}}$, this Journal, vol. 77 (2012), no. 3, pp. 934–946.Google Scholar