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Arity and alternation in second-order logic
1996
Annals of Pure and Applied Logic
We investigate the expressive power of second-order logic over finite structures, when two limitations are imposed. Let SAA@, n)(AA(k, n)) be the set of second-order formulas such that the arity of the relation variables is bounded by k and the number of alternations of (both first-order and) second-order quantification is bounded by n. We show that this imposes a proper hierarchy on second-order logic, i.e. for every k, n there are problems not definable in AA(k, n) but definable in AA(k + cl,
doi:10.1016/0168-0072(95)00013-5
fatcat:b3iwj3l4sze6plwzp7jw2nmvsu