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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An upper cardinal bound on absolute E-rings


Authors: Daniel Herden and Saharon Shelah
Journal: Proc. Amer. Math. Soc. 137 (2009), 2843-2847
MSC (2000): Primary 20K30, 03E55, 03E75; Secondary 13C05, 03C25
Published electronically: February 24, 2009
MathSciNet review: 2506440
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Abstract: We show that for every abelian group $ A$ of cardinality $ \ge\kappa(\omega)$ there exists a generic extension of the universe, where $ A$ is countable with $ 2^{\aleph_0}$ injective endomorphisms. As an immediate consequence of this result there are no absolute E-rings of cardinality $ \ge \kappa(\omega)$. This paper does not require any specific prior knowledge of forcing or model theory and can be considered accessible also for graduate students.


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Additional Information

Daniel Herden
Affiliation: Fachbereich Mathematik, Universität Duisburg-Essen, Campus Essen, 45117 Essen, Germany
Email: Daniel.Herden@uni-due.de

Saharon Shelah
Affiliation: Einstein Institute of Mathematics, Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 91904, Israel – and – Center for Mathematical Sciences Research, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019
Email: Shelah@math.huji.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09842-6
PII: S 0002-9939(09)09842-6
Received by editor(s): March 12, 2008
Received by editor(s) in revised form: November 23, 2008
Published electronically: February 24, 2009
Additional Notes: The first author was supported by a Wolfgang Gentner Minerva Fellowship.
The second author was supported by project No. I-706-54.6/2001 of the German-Israeli Foundation for Scientific Research and Development.
Communicated by: Julia Knight
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.