The Journal of Symbolic Logic

Research Article

The hierarchy theorem for second order generalized quantifiers

Juha Kontinen

University of Helsinki, Department of Mathematics and Statistics, P.O. Box 68 (Gustaf Hällströmin Katu 2b), Helsinki, Fin-00014, Finland. E-mail: juha.kontinen@helsinki.fi

Abstract

We study definability of second order generalized quantifiers on finite structures. Our main result says that for every second order type t there exists a second order generalized quantifier of type t which is not definable in the extension of second order logic by all second order generalized quantifiers of types lower than t.

(Received April 08 2004)

(Accepted September 12 2005)