Journal of Symbolic Logic

The hierarchy theorem for second order generalized quantifiers

Juha Kontinen

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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.

Article information

Source
J. Symbolic Logic Volume 71, Issue 1 (2006), 188-202.

Dates
First available in Project Euclid: 22 February 2006

Permanent link to this document
http://projecteuclid.org/euclid.jsl/1140641168

Digital Object Identifier
doi:10.2178/jsl/1140641168

Mathematical Reviews number (MathSciNet)
MR2210061

Zentralblatt MATH identifier
05038893

Subjects
Primary: 03C80: Logic with extra quantifiers and operators [See also 03B42, 03B44, 03B45, 03B48]
Secondary: 03C13: Finite structures [See also 68Q15, 68Q19] 03C85: Second- and higher-order model theory

Citation

Kontinen, Juha. The hierarchy theorem for second order generalized quantifiers. J. Symbolic Logic 71 (2006), no. 1, 188--202. doi:10.2178/jsl/1140641168. http://projecteuclid.org/euclid.jsl/1140641168.


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References

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  • L. Hella, K. Luosto, and J. Väänänen The hierarchy theorem for generalized quantifiers, Journal of Symbolic Logic, vol. 61 (1996), no. 3, pp. 802--817.
  • J. Kontinen Definability of second order generalized quantifiers, Archive for Mathematical Logic, to appear.