Almost-free E-rings of cardinality aleph_1

dc.creatorGöbel, Rüdiger
dc.creatorShelah, Saharon
dc.creatorStrüngmann, Lutz
dc.date2001-12-20
dc.date.accessioned2026-07-07T04:45:23Z
dc.date.available2026-07-07T04:45:23Z
dc.descriptionAn E-ring is a unital ring R such that every endomorphism of the underlying abelian group R^+ is multiplication by some ring-element. The existence of almost-free E-rings of cardinality greater than 2^{aleph_0} is undecidable in ZFC. While they exist in Goedel's universe, they do not exist in other models of set theory. For a regular cardinal aleph_1 <= lambda <= 2^{aleph_0} we construct E-rings of cardinality lambda in ZFC which have aleph_1-free additive structure. For lambda = aleph_1 we therefore obtain the existence of almost-free E-rings of cardinality aleph_1 in ZFC.
dc.identifierhttps://arxiv.org/abs/math/0112214
dc.identifierhttp://arxiv.org/abs/math/0112214
dc.identifierCanad. J. Math. 55 No. 4 (2003) 750--765
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62932
dc.subjectLogic
dc.subjectRings and Algebras
dc.titleAlmost-free E-rings of cardinality aleph_1
dc.typetext

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