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On Preservation Theorems for Two-Variable Logic
Mathematical Logic Quarterly 45 (3):315-325 (1999)
Abstract
We show that the existential preservation theorem fails for two-variable first-order logic FO2. It is known that for all k ≥ 3, FOk does not have an existential preservation theorem, so this settles the last open case, answering a question of Andreka, van Benthem, and Németi. In contrast, we prove that the homomorphism preservation theorem holds for FO2Author's Profile
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Citations of this work
On the restraining power of guards.Erich Grädel - 1999 - Journal of Symbolic Logic 64 (4):1719-1742.
Omitting types for finite variable fragments and complete representations of algebras.Hajnal Andréka, István Németi & Tarek Sayed Ahmed - 2008 - Journal of Symbolic Logic 73 (1):65-89.
Some aspects of model theory and finite structures.Eric Rosen - 2002 - Bulletin of Symbolic Logic 8 (3):380-403.
References found in this work
Modal logic and classical logic.Johan van Benthem - 1983 - Atlantic Highlands, N.J.: Distributed in the U.S.A. by Humanities Press.
On languages with two variables.Michael Mortimer - 1975 - Mathematical Logic Quarterly 21 (1):135-140.
On the decision problem for two-variable first-order logic.Erich Grädel, Phokion G. Kolaitis & Moshe Y. Vardi - 1997 - Bulletin of Symbolic Logic 3 (1):53-69.
Modal logic over finite structures.Eric Rosen - 1997 - Journal of Logic, Language and Information 6 (4):427-439.
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