Infinitary Axiomatizability of Slender and Cotorsion-Free Groups

1999/10/28 by Oren Kolman, Saharon Shelah, Kolman, Oren +1
Mathematics · #03C75 #20A05 #20A15 (Primary) 03C55 #20K20 (Secondary) #Advanced Topics in Algebra #FOS: Mathematics #Geometric and Algebraic Topology #Logic (math.LO) #Rings, Modules, and Algebras #math.LO #msc:03C55 #msc:03C75 #msc:20A05 #msc:20A15 #msc:20K20

paper · pdf · doi:10.48550/arxiv.math/9910162

published as Bull. Belg. Math. Soc. Simon Stevin 7 No. 4 (2000) 623--629

arxiv created 1999/10/28 · openalex publication_date 1999/10/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The classes of slender and cotorsion-free abelian groups are axiomatizable in the infinitary logics L_infty,omega1 and L_infty,omega, respectively. The Baer-Specker group Z^omega is not L_infty,omega1-equivalent to a slender group.

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• Modules and Infinitary Logics
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