Torsion-free abelian groups are faithfully Borel complete and pure embeddability is a complete analytic quasi-order

2023/12/07 by Paolini, Gianluca, Shelah, Saharon
#03E15 #20K20 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2312.04162

Abstract

In [9] we proved that the space of countable torsion-free abelian groups is Borel complete. In this paper we show that our construction from [9] satisfies several additional properties of interest. We deduce from this that countable torsion-free abelian groups are faithfully Borel complete, in fact, more strongly, we can \mathfrakL_{ω1, ω}-interpret countable graphs in them. Secondly, we show that the relation of pure embeddability (equiv., elementary embeddability) among countable models of Th(ℤ^(ω)) is a complete analytic quasi-order.

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