A dichotomy in classifying quantifiers for finite models
Logic
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0405091,
title = {A dichotomy in classifying quantifiers for finite models},
author = {Mor Doron and Saharon Shelah},
journal= {arXiv preprint arXiv:math/0405091},
year = {2007}
}