A Reiterman theorem for pseudovarieties of finite first-order structures (Q1921405)
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scientific article; zbMATH DE number 920798
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Reiterman theorem for pseudovarieties of finite first-order structures |
scientific article; zbMATH DE number 920798 |
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A Reiterman theorem for pseudovarieties of finite first-order structures (English)
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27 August 1996
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Birkhoff's Theorem on classes of algebras being varieties was generalized by J. Reiterman as follows: a class of finite algebras is a pseudovariety (that is, it is closed under taking subalgebras, homomorphic images and finitary direct products) iff it is defined by a set of equations in the appropriate free profinite structures. Here, the result is generalized to first-order structures: under certain natural conditions of finiteness and non-emptiness, pseudovarieties of first-order structures are defined by relational identities (pseudoidentities) in some relatively free profinite structures.
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pseudoidentities
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pseudovariety
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finitary direct products
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free profinite structures
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first-order structures
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relational identities
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