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1 results

  • Model companions for finitely generated universal Horn classes

  • Stanley Burris
  • Journal:
    The Journal of Symbolic Logic / Volume 49 / Issue 1 / March 1984
    Published online by Cambridge University Press:
    12 March 2014, pp. 68-74
    Print publication:
    March 1984

  • In an earlier paper we proved that a universal Horn class generated by finitely many finite structures has a model companion. If the language has only finitely many fundamental operations then the theory of the model companion admits a primitive recursive elimination of quantifiers and is primitive recursive. The theory of the model companion is ℵ0-categorical iff it is complete iff the universal Horn class has the joint embedding property iff the universal Horn class is generated by a single finite structure. In the last section we look at structure theorems for the model companions of universal Horn classes generated by functionally complete algebras, in particular for the cases of rings and groups.