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The hierarchy theorem for second order generalized quantifiers

Published online by Cambridge University Press:  12 March 2014

Juha Kontinen
Juha Kontinen*
Affiliation:
University of Helsinki, Department of Mathematics and Statistics, P.O. Box 68 (Gustaf Hällströmin Katu 2b), Helsinki, Fin-00014, Finland. E-mail: [email protected]
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 1 , March 2006 , pp. 188 - 202
Copyright
Copyright © Association for Symbolic Logic 2006

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References

REFERENCES

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[5]Kontinen, J., Definability of second order generalized quantifiers, Archive for Mathematical Logic, to appear.Google Scholar