The hierarchy theorem for second order generalized quantifiers
Source: J. Symbolic Logic
Volume 71, Issue 1
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.
Full-text: Access denied (no subscription
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
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
A. Andersson On second-order generalized quantifiers and finite structures, Annals of Pure and Applied Logic, vol. 115 (2002), no. 1--3, pp. 1--32.
W. Burnside Theory of Groups of Finite Order, 2nd ed., Dover Publications Inc., New York,1955.
Mathematical Reviews (MathSciNet): MR69818
R. Fagin The number of finite relational structures, Discrete Mathematics, vol. 19 (1977), no. 1, pp. 17--21.
Mathematical Reviews (MathSciNet): MR457234
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.