Infinite Abelian groups

Isotype subgroups of totally projective groups

P(I) denotes the abelian group of integer-valuated functions defined on the set I, Pκ (I) its subgroup consisting of all elements, which support has size less than the infinite cardinal κ and Qκ (I) the quotient P(I)/Pκ(I). We formulate a statement I(κ) in the following way: For an arbitrary set I you can lift every homomorphism from P (ℕ) to Qκ(I) to a homomorphism from P(ℕ) to P(I). Using Martin's Axiom we show, that L(ℵ) is independent of ZFC.

Infinite Abelian groups

Citations

Isotype subgroups of totally projective groups

Martinaxiom und die Beschreibung gewisser Homomorphismen in der Theorie der ℵ1-freien abelschen Gruppen

Weak compactness and the structure of Ext(A,ℤ)

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