Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-09T05:27:44.524Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Andersson, A., On second-order generalized quantifiers and finite structures, Annals of Pure and Applied Logic, vol. 115 (2002), no. 1–3, pp. 1–32.CrossRefGoogle Scholar
[2]Burnside, W., Theory of Groups of Finite Order, 2nd ed., Dover Publications Inc., New York, 1955.Google Scholar
[3]Fagin, R., The number of finite relational structures, Discrete Mathematics, vol. 19 (1977), no. 1, pp. 17–21.CrossRefGoogle Scholar
[4]Hella, L., Luosto, K., and Väänänen, J., The hierarchy theorem for generalized quantifiers, this Journal, vol. 61 (1996), no. 3, pp. 802–817.Google Scholar
[5]Kontinen, J., Definability of second order generalized quantifiers, Archive for Mathematical Logic, to appear.Google Scholar