Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 71, Issue 1 (2006), 188-202.
The hierarchy theorem for second order generalized quantifiers
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.
J. Symbolic Logic Volume 71, Issue 1 (2006), 188-202.
First available in Project Euclid: 22 February 2006
Permanent link to this document
Digital Object Identifier
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. https://projecteuclid.org/euclid.jsl/1140641168.