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An upper cardinal bound on absolute E-rings

We show that for every abelian group A of cardinality ≥ κ(ω) there exists a generic extension of the universe, where A is countable with 2 N 0 injective endomorphisms. As an immediate consequence of this result there are no absolute E-rings of cardinality > κ(ω). This paper does not require any specific prior knowledge of forcing or model theory and can be considered accessible also for graduate students.