Journal of Symbolic Logic

A dichotomy in classifying quantifiers for finite models

Mor Doron and Saharon Shelah

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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.

Article information

Source
J. Symbolic Logic, Volume 70, Issue 4 (2005), 1297-1324.

Dates
First available in Project Euclid: 18 October 2005

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1129642126

Digital Object Identifier
doi:10.2178/jsl/1129642126

Mathematical Reviews number (MathSciNet)
MR2194248

Zentralblatt MATH identifier
1108.03040

Citation

Shelah, Saharon; Doron, Mor. A dichotomy in classifying quantifiers for finite models. J. Symbolic Logic 70 (2005), no. 4, 1297--1324. doi:10.2178/jsl/1129642126. https://projecteuclid.org/euclid.jsl/1129642126


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References

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