Vectorization hierarchies of some graph quantifiers
If \(Q\) is a generalized quantifier and \(k\geq 1\), denote by \(Q^k\) the \(k\)th vectorization of \(Q\). The vectorization hierarchy of \(Q\) is unbounded if there are arbitrarily large natural numbers \(k\) such that \(Q^k\) is not expressible in the extension \(\text{FO} (\{Q^l|l<k\})\) of first-order logic FO. Conditions on \(Q\) are presented that guarantee that the vectorization hierarchy is unbounded. Applications to concrete quantifiers are given.
scientific article; zbMATH DE number 1463219