Abstract
In this paper (except in Section 5) all quantifiers are assumedto be so called simple unaryquantifiers, and all models are assumedto be finite. We give a necessary and sufficientcondition for a quantifier to be definablein terms of monotone quantifiers. For amonotone quantifier we give a necessaryand sufficient condition for beingdefinable in terms of a given set of bounded monotonequantifiers. Finally, we give a necessaryand sufficient condition for a monotonequantifier to be definable in terms of agiven monotone quantifier.Our analysis shows that the quantifier’’at least one half” and its relatives behavedifferently than other monotone quantifiers.
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Väänänen, J. Unary Quantifiers on Finite Models. Journal of Logic, Language and Information 6, 275–304 (1997). https://doi.org/10.1023/A:1008209019899
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DOI: https://doi.org/10.1023/A:1008209019899