Between Whitehead groups and uniformization

2022/03/23 by Poór, Márk, Shelah, Saharon
#FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)

paper · doi:10.48550/arxiv.2203.12585

Abstract

For a given stationary set S of countable ordinals we prove (in ZFC) that the assertion "every S-ladder system has ℵ₀-uniformization" is equivalent to "every strongly ℵ₁-free abelian group of cardinality ℵ₁ with non-freeness invariant ⊆ S is ℵ₁-coseparable, i.e. Ext(G, ⊕_i=0^∞ \mathbb Z)=0 (in particular Whitehead, i.e. Ext(G, \mathbb Z)=0)". This solves problems B3 and B4 from Eklof and Mekler's monograph.

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