An upper cardinal bound on absolute E-rings
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- by Daniel Herden and Saharon Shelah PDF
- Proc. Amer. Math. Soc. 137 (2009), 2843-2847 Request permission
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.References
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Additional Information
- Daniel Herden
- Affiliation: Fachbereich Mathematik, Universität Duisburg-Essen, Campus Essen, 45117 Essen, Germany
- MR Author ID: 810921
- 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
- MR Author ID: 160185
- ORCID: 0000-0003-0462-3152
- Email: Shelah@math.huji.ac.il
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 2843-2847
- MSC (2000): Primary 20K30, 03E55, 03E75; Secondary 13C05, 03C25
- DOI: https://doi.org/10.1090/S0002-9939-09-09842-6
- MathSciNet review: 2506440