On the structure of Ext(A,Z) in ZFC+

DOI10.2307/2274216zbMath0579.20054OpenAlexW1556132717MaRDI QIDQ3701648

Saharon Shelah, Gershon Sageev

Publication date: 1985

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2274216

zbMATH Keywords

ZFCGCHregular cardinal\(V=L\)successor cardinalalmost free abelian grouptorsion free abelian groups

Mathematics Subject Classification ID

Consistency and independence results (03E35) Inner models, including constructibility, ordinal definability, and core models (03E45) Large cardinals (03E55) Continuum hypothesis and Martin's axiom (03E50) Torsion-free groups, infinite rank (20K20) Extensions of abelian groups (20K35)

Related Items

Unnamed Item ⋮ On strongly-non-reflexive groups ⋮ On the structure of \(Ext_ p(G,{\mathbb{Z}})\) ⋮ On the rank of Ext ⋮ The affinity of set theory and abelian group theory. ⋮ Abelian groups ⋮ On the \(p\)-rank of Ext ⋮ Every coseparable group may be free

Cites Work

• Abelian group extensions and the axiom of constructibility
• The consistency of \(\mathrm{Ext}\,(G,\mathbb{Z})=\mathbb{Q}\)
• Whitehead groups may not be free even assuming CH. II
• Infinite Abelian groups, Whitehead problem and some constructions
• On Banach spaces which contain \(\ell^1(\tau)\) and types of measures on compact spaces
• The structure of Ext\((A,\mathbb{Z})\) and \(V=L\)
• Whitehead groups may be not free, even assuming CH. I
• On uncountable Abelian groups
• Whitehead's Problem is Undecidable