The strict Borel reducibility conjecture for positive-rank torsion-free abelian groups

Let n1n+\bigsqcup_{n\geq 1} \cong_n^+ denote the disjoint union of the isomorphism relations n+\cong_n^+ on the corresponding spaces of torsion-free abelian groups, and let EE_\infty be the universal countable Borel equivalence relation. The strict reducibility conjecture.

(n1n+)<BE.\left(\bigsqcup_{n\geq 1} \cong_n^+ \right)<_B E_\infty.

This asks whether the combined classification problem for these groups is strictly below the universal countable Borel equivalence relation, extending the analogous result for torsion-free abelian groups without the positive superscript. The source gives no resolution.

Sources & referencesView supporting material

Primary source

Paul Ellis, “The Classification Problem for Simple Unital Finite Rank Dimension Groups”, arXiv:1709.06684 (2017).

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