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THE TREE PROPERTY UP TO אω+1

Published online by Cambridge University Press:  25 June 2014

ITAY NEEMAN
ITAY NEEMAN*
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF CALIFORNIA LOS ANGELES LOS ANGELES, CA 90095-1555E-mail: ineeman@math.ucla.edu
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Abstract

Assuming ω supercompact cardinals we force to obtain a model where the tree property holds both at אω+1, and at אn for all 2 ≤ n < ω. A model with the former was obtained by Magidor–Shelah from a large cardinal assumption above a huge cardinal, and recently by Sinapova from ω supercompact cardinals. A model with the latter was obtained by Cummings–Foreman from ω supercompact cardinals. Our model, where the two hold simultaneously, is another step toward the goal of obtaining the tree property on increasingly large intervals of successor cardinals.

Keywords

03E3503E0503E55Aronszajn treestree propertysupercompact cardinals
Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 2 , June 2014 , pp. 429 - 459
Copyright
Copyright © The Association for Symbolic Logic 2014 

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References

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