An upper cardinal bound on absolute E-rings

by Herden and Shelah. [HeSh:930]
Proc American Math Soc, 2009
We show that for every abelian group A of cardinality >= 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 >= 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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