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Published online by Cambridge University Press: 12 March 2014
We consider a family of finite universes. The second order existential quantifier Qℜ means for each U Є
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 Qℜ, either Qℜ is interpretable by quantifying over subsets of U and one to one functions on U both of bounded order, or the logic L(Qℜ) (first order logic plus the quantifier Qℜ) is undecidable.
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