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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


New criteria for freeness in abelian groups. II

Author: Paul Hill
Journal: Trans. Amer. Math. Soc. 196 (1974), 191-201
MSC: Primary 20K20
MathSciNet review: 0352294
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Abstract: A new criterion is established for an abelian group to be free. The criterion is in terms of an ascending chain of free subgroups and is dependent upon a new class of torsion-free groups. The result leads to the construction, for each positive integer n, of a group $ {G_n}$ of cardinality $ {\aleph _n}$ that is not free but is $ {\aleph _n}$-free. A conjecture in infinitary logic concerning free abelian groups is also verified.

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PII: S 0002-9947(1974)0352294-8
Keywords: Smooth chain of free groups, $ {\aleph _n}$-free, $ {\beth _n}$-free groups, non-free $ {\aleph _n}$-free groups, equivalence in $ {L_{\infty \kappa }}$
Article copyright: © Copyright 1974 American Mathematical Society

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