Borel Complexity of the Isomorphism Relation of Archimedean Orders in Finitely Generated Groups

2024/03/17 by Antoine Poulin, Poulin, Antoine · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #Mathematical and Theoretical Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2403.11326

openalex publication_date 2024/03/17 · openalex created_date 2024/03/20 · openalex updated_date 2026/07/28

Abstract

In 2020, Calderoni, Marker, Motto Ros and Shani asked what the Borel complexity of the isomorphism relation of Archimedean orders on ℚⁿ is. We answer this question by proving that the isomorphism relation of Archimedean orders on ℤⁿ is not hyperfinite when n ≥ 3 and not treeable when n ≥ 4. As a corollary, we get that the isomorphism relation of Archimedean orders on ℚⁿ is not hyperfinite when n ≥ 3 and not treeable when n ≥ 4.

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