GCH implies the existence of many rigid almost free abelian groups
| dc.creator | Göbel, Rüdiger | |
| dc.creator | Shelah, Saharon | |
| dc.date | 2000-11-22 | |
| dc.date.accessioned | 2026-07-07T04:38:46Z | |
| dc.date.available | 2026-07-07T04:38:46Z | |
| dc.description | We begin with the existence of groups with trivial duals for cardinals aleph_n (n in omega). Then we derive results about strongly aleph_n-free abelian groups of cardinality aleph_n (n in omega) with prescribed free, countable endomorphism ring. Finally we use combinatorial results of [Sh:108], [Sh:141] to give similar answers for cardinals >aleph_omega. As in Magidor and Shelah [MgSh:204], a paper concerned with the existence of kappa-free, non-free abelian groups of cardinality kappa, the induction argument breaks down at aleph_omega. Recall that aleph_omega is the first singular cardinal and such groups of cardinality aleph_omega do not exist by the well-known Singular Compactness Theorem (see [Sh:52]). | |
| dc.identifier | https://arxiv.org/abs/math/0011185 | |
| dc.identifier | http://arxiv.org/abs/math/0011185 | |
| dc.identifier | Proceedings of the Conference on Abelian Groups in Colorado Springs (1995), volume 182 of Lecture Notes in Pure and Applied Math., pp 253-271, Marcel Dekker 1996 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60415 | |
| dc.subject | Group Theory | |
| dc.subject | Logic | |
| dc.title | GCH implies the existence of many rigid almost free abelian groups | |
| dc.type | text |