A Reiterman theorem for pseudovarieties of finite first-order structures

Jean-Eric Pin (1) , Pascal Weil (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

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).

Mots clés: Reiterman's theorem; semigroup varieties; first order logic

Domaines: Logique en informatique [cs.LO]; Mathématique discrète [cs.DM]; Logique [math.LO]; Théorie des groupes [math.GR]

Jean-Eric Pin, Pascal Weil. A Reiterman theorem for pseudovarieties of finite first-order structures. Algebra Universalis, 1996, 35 (4), pp.577-595. ⟨hal-00143951⟩