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THE TREE PROPERTY AT ${\aleph _{{\omega ^2} + 1}}$ AND ${\aleph _{{\omega ^2} + 2}}$

Published online by Cambridge University Press:  01 August 2018

DIMA SINAPOVA  and
SPENCER UNGER
DIMA SINAPOVA
Affiliation:
DEPARTMENT OF MATHEMATICS, STATISTICS, AND COMPUTER SCIENCE UNIVERSITY OF ILLINOIS AT CHICAGO CHICAGO, IL60607-7045, USAE-mail:sinapova@math.uic.edu
SPENCER UNGER
Affiliation:
SCHOOL OF MATHEMATICAL SCIENCES TEL AVIV UNIVERSITY TEL AVIV69978, ISRAELE-mail:sunger@math.ucla.edu
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Abstract

We show that from large cardinals it is consistent to have the tree property simultaneously at ${\aleph _{{\omega ^2} + 1}}$ and ${\aleph _{{\omega ^2} + 2}}$ with ${\aleph _{{\omega ^2}}}$ strong limit.

Keywords

03E0503E3503E55tree propertyPrikry forcingsingular cardinals hypothesis
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 2 , June 2018 , pp. 669 - 682
Copyright
Copyright © The Association for Symbolic Logic 2018 

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