Infinitary axiomatizability of slender and cotorsion-free groups

Saharon Shelah; Oren Kolman

doi:10.36045/bbms/1103055621

Infinitary axiomatizability of slender and cotorsion-free groups

Saharon Shelah^*
, Oren Kolman

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

The classes of slender and cotorsion-free abelian groups are axiomatizable in the infinitary logics L_∞ω1 and L_∞ω, respectively. The Baer-Specker group ℤ^ω is not L_∞ω1-equivalent to a slender group.

Original language	English
Pages (from-to)	623-629
Number of pages	7
Journal	Bulletin of the Belgian Mathematical Society - Simon Stevin
Volume	7
Issue number	4
DOIs	https://doi.org/10.36045/bbms/1103055621
State	Published - 2000

Keywords

Axiomatizability
Baer-Specker group
Cotorsion-free
Infinitary logic
Infinite abelian group
Slender

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10.36045/bbms/1103055621

Cite this

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title = "Infinitary axiomatizability of slender and cotorsion-free groups",

abstract = "The classes of slender and cotorsion-free abelian groups are axiomatizable in the infinitary logics L∞ω1 and L∞ω, respectively. The Baer-Specker group ℤω is not L∞ω1-equivalent to a slender group.",

keywords = "Axiomatizability, Baer-Specker group, Cotorsion-free, Infinitary logic, Infinite abelian group, Slender",

author = "Saharon Shelah and Oren Kolman",

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AU - Kolman, Oren

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KW - Axiomatizability

KW - Baer-Specker group

KW - Cotorsion-free

KW - Infinitary logic

KW - Infinite abelian group

KW - Slender

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JO - Bulletin of the Belgian Mathematical Society - Simon Stevin

JF - Bulletin of the Belgian Mathematical Society - Simon Stevin

IS - 4

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Infinitary axiomatizability of slender and cotorsion-free groups

Abstract

Keywords

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