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Group radicals and strongly compact cardinals

Authors: Joan Bagaria and Menachem Magidor
Journal: Trans. Amer. Math. Soc. 366 (2014), 1857-1877
MSC (2010): Primary 03E35, 03E55, 16S90, 18E40; Secondary 03E75, 20Kxx
Published electronically: November 25, 2013
MathSciNet review: 3152715
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Abstract: We answer some natural questions about group radicals and torsion classes, which involve the existence of measurable cardinals, by constructing, relative to the existence of a supercompact cardinal, a model of ZFC in which the first $ \omega _1$-strongly compact cardinal is singular.

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Additional Information

Joan Bagaria
Affiliation: ICREA (Institució Catalana de Recerca i Estudis Avançats) – and – Departament de Lògica, Història i Filosofia de la Ciència, Universitat de Barcelona, Montalegre 6, 08001 Barcelona, Catalonia, Spain

Menachem Magidor
Affiliation: Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 91904, Israel

Keywords: Group radical, torsion class, infinite abelian group, measurable cardinal, strongly compact cardinal, supercompact cardinal, Radin forcing.
Received by editor(s): April 5, 2011
Received by editor(s) in revised form: September 16, 2011, January 16, 2012, and May 3, 2012
Published electronically: November 25, 2013
Additional Notes: The research of the first author was partially supported by the Spanish Ministry of Science and Innovation under grants MTM2008-03389 and MTM2011-25229, and by the Generalitat de Catalunya (Catalan Government) under grant 2009 SGR 187
The research of the second author was supported by the Israel Science Foundation grant 817/11. Part of this work was carried out while the authors were visiting the Mittag-Leffler Institut and the Mathematisches Forschungsinstitut Oberwolfach, whose hospitality is gratefully acknowledged.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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