The Structure of Groups Which are Almost the Direct Sum of Countable Abelian Groups

DOI10.2307/2000783zbMath0629.20024OpenAlexW4245985011MaRDI QIDQ3765973

Alan H. Mekler

Publication date: 1987

Full work available at URL: https://doi.org/10.2307/2000783

zbMATH Keywords

proper forcing axiomstandard formconsistentMartin's Axiomdirect sum of cyclicstorsion-free abelian groupsstrong decomposition\(\omega _ 1\)- separable abelian groups\(\omega _ 1\)-filtration\(\omega _ 1\)-free groupsweak Fuchs-5 groups

Mathematics Subject Classification ID

Consistency and independence results (03E35) Continuum hypothesis and Martin's axiom (03E50) Applications of set theory (03E75) Torsion-free groups, infinite rank (20K20) Extensions of abelian groups (20K35)

Related Items (3)

Totally Crawley groups ⋮ Abelian groups ⋮ Obituary: Alan Mekler

Cites Work

• Crawley's problem on the unique \(\omega\)-elongation of p-groups is undecidable
• Proper forcing
• Infinite Abelian groups, Whitehead problem and some constructions
• On constructing indecomposable groups in L
• C.c.c. forcing without combinatorics
• The Structure of ω 1 -Separable Groups
• On p^ω+1 -Projective p -Groups
• Infinitary equivalence of abelian groups
• How to Construct Almost Free Groups
• On the Decomposition of Groups
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