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The Hierarchy Theorem for Generalized Quantifiers
Lauri Hella, Kerkko Luosto and Jouko Väänänen
The Journal of Symbolic Logic
Vol. 61, No. 3 (Sep., 1996), pp. 802-817
Published by: Association for Symbolic Logic
Stable URL: http://www.jstor.org/stable/2275786
Page Count: 16
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The concept of a generalized quantifier of a given similarity type was defined in . Our main result says that on finite structures different similarity types give rise to different classes of generalized quantifiers. More exactly, for every similarity type t there is a generalized quantifier of type t which is not definable in the extension of first order logic by all generalized quantifiers of type smaller than t. This was proved for unary similarity types by Per Lindström  with a counting argument. We extend his method to arbitrary similarity types.
The Journal of Symbolic Logic © 1996 Association for Symbolic Logic