Birkhoff's variety theorem in many sorts (Q1762479)
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scientific article; zbMATH DE number 6110488
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Birkhoff's variety theorem in many sorts |
scientific article; zbMATH DE number 6110488 |
Statements
Birkhoff's variety theorem in many sorts (English)
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27 November 2012
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In this paper, Birkhoff's characterization of equational classes is proved to generalize the case of finitely many sorts: For every set \(S\) of sorts and every \(S\)-sorted signature \(\Sigma\), the equational classes of \(\Sigma\)-algebras are precisely the full subcategories of \(\Sigma\)-Alg closed under products, subalgebras, regular quotients,and directed unions. For infinitely sorted algebras, closure under directed unions needs to be added.
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many-sorted algebras
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Birkhoff variety theorem
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0.91378117
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0.91054666
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0.9073365
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0.8962636
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0.89481986
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