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2 results

  • Existentially closed models of the theory of artinian local rings

  • Hans Schoutens
  • Journal:
    The Journal of Symbolic Logic / Volume 64 / Issue 2 / June 1999
    Published online by Cambridge University Press:
    12 March 2014, pp. 825-845
    Print publication:
    June 1999

  • The class of all Artinian local rings of length at most l is ∀2-elementary, axiomatised by a finite set of axioms τtl. We show that its existentially closed models are Gorenstein. of length exactly l and their residue fields are algebraically closed, and, conversely, every existentially closed model is of this form. The theory oτl of all Artinian local Gorenstein rings of length l with algebraically closed residue field is model complete and the theory τtl is companionable, with model-companion oτl.