# 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)

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} }