Journal of Symbolic Logic

The hierarchy theorem for second order generalized quantifiers

Juha Kontinen

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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

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

First available in Project Euclid: 22 February 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

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