Unary Quantifiers on Finite Models


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Abstract

In this paper (except in Section 5) all quantifiers are assumed to be so called simple unary quantifiers, and all models are assumed to be finite. We give a necessary and sufficient condition for a quantifier to be definable in terms of monotone quantifiers. For a monotone quantifier we give a necessary and sufficient condition for being definable in terms of a given set of bounded monotone quantifiers. Finally, we give a necessary and sufficient condition for a monotone quantifier to be definable in terms of a given monotone quantifier. Our analysis shows that the quantifier “at least one half” and its relatives behave differently than other monotone quantifiers.

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