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THE STRONG TREE PROPERTY AT SUCCESSORS OF SINGULAR CARDINALS

Published online by Cambridge University Press:  17 April 2014

LAURA FONTANELLA
LAURA FONTANELLA*
Affiliation:
EQUIPE DE LOGIQUE MATHÉMATIQUE, UNIVERSITÉ PARIS DIDEROT PARIS 7, UFR DE MATHÉMATIQUES CASE 7012, SITE CHEVALERET, 75205 PARIS CEDEX 13, FRANCE, KURT GÖDEL RESEARCH CENTER FOR MATHEMATICAL LOGIC, UNIVERSITY OF VIENNA, DEPARTMENT OF MATHEMATICS, WÄHRINGER STRASSE 25, VIENNA 1090, AUSTRIAE-mail: fontanl6@univie.ac.at, URL:http://www.logique.jussieu.fr/∼fontanella
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Abstract

An inaccessible cardinal is strongly compact if, and only if, it satisfies the strong tree property. We prove that if there is a model of ZFC with infinitely many supercompact cardinals, then there is a model of ZFC where ${\aleph _{\omega + 1}}$ has the strong tree property. Moreover, we prove that every successor of a singular limit of strongly compact cardinals has the strong tree property.

Keywords

Tree propertylarge cardinalsforcing03E55.
Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 1 , March 2014 , pp. 193 - 207
Copyright
Copyright © Association for Symbolic Logic 2014 

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