Equivalents for a quasivariety to be generated by a single structure (Q1005982)
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scientific article; zbMATH DE number 5529417
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Equivalents for a quasivariety to be generated by a single structure |
scientific article; zbMATH DE number 5529417 |
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Equivalents for a quasivariety to be generated by a single structure (English)
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17 March 2009
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In \textit{A. I. Mal'tsev}'s article [Algebra Logika 5, No. 3, 3--9 (1966; Zbl 0248.08006)], there can be found a condition for a quasivariety to be generated by a single structure, namely, the embedding property for nontrivial structures, which states that if \(A,B\in \mathcal{K}\) are nontrivial, then there exists \(C\in \mathcal{K}\) such that \(A,B\) are embeddable into \(C.\) In this paper, the authors present more equivalent conditions for a quasivariety of structures to be generated by a single structure, thus equivalent to Mal'tsev's condition.
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quasivariety
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embedding property
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Los-Suszko rule
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free product
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generation by a single structure
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