On uncountable Abelian groups

DOI10.1007/BF02760461zbMath0412.20047MaRDI QIDQ1260187

Saharon Shelah

Publication date: 1979

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Whitehead groupMartin's axiomAxiom of constructibilitycountable direct sum of integersdirect summand of countable indexhereditarily separable groups

Mathematics Subject Classification ID

Consistency and independence results (03E35) Inner models, including constructibility, ordinal definability, and core models (03E45) Continuum hypothesis and Martin's axiom (03E50) Torsion-free groups, infinite rank (20K20) Axiomatics of classical set theory and its fragments (03E30) Direct sums, direct products, etc. for abelian groups (20K25) Subgroups of abelian groups (20K27) Metamathematical considerations in group theory (20A10)

Related Items

On the structure of Ext(A,Z) in ZFC⁺, Unnamed Item, Hereditarily separable groups and monochromatic uniformization, Uniformization principles, On the structure of \(Ext_ p(G,{\mathbb{Z}})\), On the rank of Ext, The consistency of \(\mathrm{Ext}\,(G,\mathbb{Z})=\mathbb{Q}\), Whitehead groups may not be free even assuming CH. II, Set Theory Generated by Abelian Group Theory, The affinity of set theory and abelian group theory., Prescribing endomorphism algebras of \(\aleph_n\)-free modules., Abelian groups, Whitehead groups may be not free, even assuming CH. I, Uniformization and the diversity of Whitehead groups, Small almost free modules with prescribed topological endomorphism rings., On reflexive modules and Abelian groups, A simple proof for a theorem of Chase

Cites Work

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• A weak version of \(\lozenge\) which follows from \(2^{\aleph_0}<2^{\aleph_1}\)
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