A dichotomy in classifying quantifiers for finite models

Details A dichotomy in classifying quantifiers for finite models A dichotomy in classifying quantifiers for finite models

2004-05-06

arxiv.org/abs/math/0405091v1

Mathematics

Logic

Scientific paper

We consider a family U of finite universes. The second order quantifier Q_R, means for each u in 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_R, ever Q_R is interpretable by quantifying over subsets of u and one to one functions on u both of bounded order, or the logic L(Q_R) (first order logic plus the quantifier Q_R) is undecidable.

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