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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