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A Model-Theoretic Characterization of Countable Direct Sums of Finite Cyclic Groups
We prove that an abelian group G is a countable direct sum of finite cyclic groups if and only if there exists a consistent existential theory Γ of abelian groups such that G is embeddable in every model of Γ.
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| Published in: | Communications in algebra 2005-09, Vol.33 (10), p.3719-3723 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Citations: | Items that this one cites |
| Online Access: | Get full text |
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| Summary: | We prove that an abelian group G is a countable direct sum of finite cyclic groups if and only if there exists a consistent existential theory Γ of abelian groups such that G is embeddable in every model of Γ. |
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| ISSN: | 0092-7872 1532-4125 |
| DOI: | 10.1080/00927870500243155 |