Notions of locality and their logical characterizations over finite models

Journal of Symbolic Logic 64 (4):1751-1773 (1999)
Many known tools for proving expressibility bounds for first-order logic are based on one of several locality properties. In this paper we characterize the relationship between those notions of locality. We note that Gaifman's locality theorem gives rise to two notions: one deals with sentences and one with open formulae. We prove that the former implies Hanf's notion of locality, which in turn implies Gaifman's locality for open formulae. Each of these implies the bounded degree property, which is one of the easiest tools for proving expressibility bounds. These results apply beyond the first-order case. We use them to derive expressibility bounds for first-order logic with unary quantifiers and counting. We also characterize the notions of locality on structures of small degree
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DOI 10.2307/2586810
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References found in this work BETA
On Winning Ehrenfeucht Games and Monadic NP.Thomas Schwentick - 1996 - Annals of Pure and Applied Logic 79 (1):61-92.

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An Existential Locality Theorem.Martin Grohe & Stefan Wöhrle - 2004 - Annals of Pure and Applied Logic 129 (1-3):131-148.
Game-Based Notions of Locality Over Finite Models.Marcelo Arenas, Pablo Barceló & Leonid Libkin - 2008 - Annals of Pure and Applied Logic 152 (1):3-30.

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