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


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.

DOI Code: 10.1285/i15900932v2n1p57

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