Journal of Symbolic Logic

A dichotomy in classifying quantifiers for finite models

Mor Doron and Saharon Shelah

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

First available in Project Euclid: 18 October 2005

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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.

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