On Preservation Theorems for Two-Variable Logic

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Mathematical Logic Quarterly 45 (3):315-325 (1999)
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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 FO2

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10.1002/malq.19990450304

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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.
Some aspects of model theory and finite structures.Eric Rosen - 2002 - Bulletin of Symbolic Logic 8 (3):380-403.

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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.
Model theory.Wilfrid Hodges - 2008 - Stanford Encyclopedia of Philosophy.
On languages with two variables.Michael Mortimer - 1975 - Mathematical Logic Quarterly 21 (1):135-140.
Modal logic over finite structures.Eric Rosen - 1997 - Journal of Logic, Language and Information 6 (4):427-439.

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