David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 64 (2):825-845 (1999)
The class of all Artinian local rings of length at most l is ∀ 2 -elementary, axiomatised by a finite set of axioms Art l . 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 Got l of all Artinian local Gorenstein rings of length l with algebraically closed residue field is model complete and the theory Art l is companionable, with model-companion Got l
|Keywords||Model Theory Existentially Closed Models Artinian Local Rings Gorenstein Rings|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Françoise Delon & Rafel Farré (1996). Some Model Theory for Almost Real Closed Fields. Journal of Symbolic Logic 61 (4):1121-1152.
Luc Bélair (1995). Anneaux de Fonctions P-Adiques. Journal of Symbolic Logic 60 (2):484-497.
Anand Pillay (2001). A Note on Existentially Closed Difference Fields with Algebraically Closed Fixed Field. Journal of Symbolic Logic 66 (2):719-721.
Paul Bankston (1999). A Hierarchy of Maps Between Compacta. Journal of Symbolic Logic 64 (4):1628-1644.
Paul C. Eklof & Hans-Christian Mez (1987). Modules of Existentially Closed Algebras. Journal of Symbolic Logic 52 (1):54-63.
Bruce I. Rose (1978). Rings Which Admit Elimination of Quantifiers. Journal of Symbolic Logic 43 (1):92-112.
Bruce I. Rose (1978). The ℵ1-Categoricity of Strictly Upper Triangular Matrix Rings Over Algebraically Closed Fields. Journal of Symbolic Logic 43 (2):250 - 259.
K.-P. Podewski & Joachim Reineke (1979). Algebraically Closed Commutative Local Rings. Journal of Symbolic Logic 44 (1):89-94.
Herbert H. J. Riedel (1988). Existentially Closed Algebras and Boolean Products. Journal of Symbolic Logic 53 (2):571-596.
Added to index2009-01-28
Total downloads5 ( #224,380 of 1,098,955 )
Recent downloads (6 months)3 ( #114,620 of 1,098,955 )
How can I increase my downloads?