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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
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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
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 

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References

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