Sh:930

• Herden, D., & Shelah, S. (2009). An upper cardinal bound on absolute E-rings. Proc. Amer. Math. Soc., 137(9), 2843–2847. DOI: 10.1090/S0002-9939-09-09842-6 MR: 2506440
• 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_O} 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.
• published version (5p)

@article{Sh:930,
 author = {Herden, Daniel and Shelah, Saharon},
 title = {{An upper cardinal bound on absolute $E$-rings}},
 journal = {Proc. Amer. Math. Soc.},
 fjournal = {Proceedings of the American Mathematical Society},
 volume = {137},
 number = {9},
 year = {2009},
 pages = {2843--2847},
 issn = {0002-9939},
 mrnumber = {2506440},
 mrclass = {20K30 (03E55 03E75)},
 doi = {10.1090/S0002-9939-09-09842-6}
}