On second-order generalized quantifiers and finite structures (Q1612478)

To extend the expressive power of first-order logic, one often adds (first-order) generalized quantifiers. In the present paper the author considers second-order generalized quantifiers. Among other things, he shows that known hierarchy results for (first-order) generalized quantifiers do not generalize. In fact, every countable logic for finite structures (and binary vocabularies) is equivalent to a fragment of some extension of first-order logic by means of a monadic, unary, and simple quantifier.