Universal abelian groups

1994/09/17 by Menachem Kojman, Saharon Shelah, Kojman, Menachem +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras #math.LO #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/9409207

published as Israel J. Math. 92 No. 1-3 (1995) 113--124

arxiv created 1994/09/17 · openalex publication_date 1994/09/17 · arxiv updated 2016/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We examine the existence of universal elements in classes of infinite abelian groups. The main method is using group invariants which are defined relative to club guessing sequences. We prove, for example: Theorem: For n≥ 2, there is a purely universal separable p-group in ℵ_n if, and only if, \cont≤ ℵ_n.

Related

• Non-existence of universal members in classes of abelian groups
• Non-existence of universals for classes like reduced torsion free abelian groups under embeddings which are not necessarily pure
• A countable universal torsion abelian group for purity
• A model theoretic solution to a problem of László Fuchs
• Generic isomorphism classes of abelian groups