A Reiterman theorem for pseudovarieties of finite first-order structures
type: Item
instance of: scholarly article
title: A Reiterman theorem for pseudovarieties of finite first-order structures
zbMATH Open document ID: 0864.03024
DOI: 10.1007/BF01243597
author: Jean-Éric Pin
author: Pascal Weil
published in: Algebra Universalis
publication date: 1996-08-27T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 03C05
Mathematics Subject Classification ID: 08B05
zbMATH DE Number: 920798
zbMATH Keywords: pseudoidentities
zbMATH Keywords: pseudovariety
zbMATH Keywords: finitary direct products
zbMATH Keywords: free profinite structures
zbMATH Keywords: first-order structures
zbMATH Keywords: relational identities
MaRDI profile type: Publication
cites work: Q4848740
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full work available at URL: https://doi.org/10.1007/bf01243597
OpenAlex ID: W2009062978
description: scientific article; zbMATH DE number 920798