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December 2005 A dichotomy in classifying quantifiers for finite models
Mor Doron, Saharon Shelah
J. Symbolic Logic 70(4): 1297-1324 (December 2005). DOI: 10.2178/jsl/1129642126

Abstract

We consider a family 𝔲 of finite universes. The second order existential quantifier Q, means for each U∈ 𝔲 quantifying over a set of n(ℜ)-place relations isomorphic to a given relation. We define a natural partial order on such quantifiers called interpretability. We show that for every Q, either Q is interpretable by quantifying over subsets of U and one to one functions on U both of bounded order, or the logic L(Q) (first order logic plus the quantifier Q) is undecidable.

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Mor Doron. Saharon Shelah. "A dichotomy in classifying quantifiers for finite models." J. Symbolic Logic 70 (4) 1297 - 1324, December 2005. https://doi.org/10.2178/jsl/1129642126

Information

Published: December 2005
First available in Project Euclid: 18 October 2005

zbMATH: 1108.03040
MathSciNet: MR2194248
Digital Object Identifier: 10.2178/jsl/1129642126

Rights: Copyright © 2005 Association for Symbolic Logic

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Vol.70 • No. 4 • December 2005
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