Yet another hierarchy theorem

Journal of Symbolic Logic 65 (2):627-640 (2000)
n + 1 nested k-ary fixed point operators are more expressive than n. This holds on finite structures for all sublogics of partial fixed point logic PFP that can express conjunction, existential quantification and deterministic transitive closure of binary relations using at most k-ary fixed point operators and that are closed against subformulas. Among those are a lot of popular fixed point logics
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DOI 10.2307/2586558
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Martin Grohe (1996). Arity Hierarchies. Annals of Pure and Applied Logic 82 (2):103-163.

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