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  1. Marcelo Arenas, Pablo Barceló & Leonid Libkin (2008). Game-Based Notions of Locality Over Finite Models. Annals of Pure and Applied Logic 152 (1):3-30.
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  2. Lauri Hella, Leonid Libkin & Juha Nurmonen (1999). Notions of Locality and Their Logical Characterizations Over Finite Models. Journal of Symbolic Logic 64 (4):1751-1773.
    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 (...)
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