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Existentially closed models of the theory of artinian local rings

Published online by Cambridge University Press:  12 March 2014

Hans Schoutens
Hans Schoutens*
Affiliation:
Mathematics Department, Wesleyan University, Middletown, CT 06459, US Fields Institute, 222 College Street, Toronto, Ontario, M5T 3J1, Canada E-mail: hschoutens@wesleyan.edu
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Abstract

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.

Keywords

model theoryexistentially closed modelsArtinian local ringsGorenstein rings
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 2 , June 1999 , pp. 825 - 845
Copyright
Copyright © Association for Symbolic Logic 1999

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References

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