Hierarchies of monadic generalized quantifiers

Journal of Symbolic Logic 65 (3):1241-1263 (2000)
Abstract
A combinatorial criterium is given when a monadic quantifier is expressible by means of universe-independent monadic quantifiers of width n. It is proved that the corresponding hierarchy does not collapse. As an application, it is shown that the second resumption (or vectorization) of the Hartig quantifier is not definable by monadic quantifiers. The techniques rely on Ramsey theory
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