Bounds for the Quantifier Depth in Finite-Variable Logics: Alternation Hierarchy

ACM Trans. Comput. Log., Volume 16, Issue Issue-in-Progress, 2015.

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Keywords:
alternation hierarchyfinite-variable logicmathematical logictheory

Abstract:

Given two structures G and H distinguishable in FOk (first-order logic with k variables), let Ak(G, H) denote the minimum alternation depth of a FOk formula distinguishing G from H. Let Ak(n) be the maximum value of Ak(G, H) over n-element structures. We prove the strictness of the quantifier alternation hierarchy of FO2 in a strong quant...More

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