# Sh:930

• Herden, D., & Shelah, S. (2009). An upper cardinal bound on absolute E-rings. Proc. Amer. Math. Soc., 137(9), 2843–2847.
• 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)
Bib entry
@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}
}