Sui reticoli di congruenze di strutture algebriche modelli di teorie universali positive

Abstract

Let T be a countable first order theory with positive axioms and the congruence extension property.The main result of this paper is the following.If T has a model whose cardinality is greater than the continuum and whose congruence lattice L is of finite length, then T has every infinite cardinality a model whose congruence lattice is isomorphic to a filter of L.Some other results about subdirecrly irreducible models are also given.The results stated above are a generalization for the theories considered of a theorem of McKenzie and Shelah.