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A Rank-Preserving Gaifman Normal Form
We introduce a rank measure for first-order logic and prove a "rank-preserving'" version of Gaifman's theorem. Compared to earlier "rank-preserving locality theorems'" (in particular, [Grohe, Kreutzer, Siebertz, JACM 2017]), our theorem is not only much simpler, but also yields formulas in exactly t
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