A Reiterman theorem for pseudovarieties of finite first-order structures ∗

@inproceedings{Pin1996ART,
  title={A Reiterman theorem for pseudovarieties of finite first-order structures ∗},
  author={Jean-{\'E}ric Pin},
  year={1996}
}
We extend Reiterman’s theorem to first-order structures: a class of finite first-order structures is a pseudovariety if and only if it is defined by a set of identities in a certain relatively free profinite structure (pseudoidentities). A well-known result of Birkhoff states that a class of algebras is a variety, that is, is closed under taking subalgebras, homomorphic images and direct products, if and only if it is equational, i.e. it is defined by a set of equations on the corresponding… CONTINUE READING