Scope dominance with upward monotone quantifiers

We give a complete characterization of the class of upward monotone generalized quantifiers ¢¡ and ¤£ over countable domains that satisfy the scheme . This generalizes the characterization of such quantifiers over finite domains, according to which the scheme holds iff ¡ is or £ is ! (excluding trivial cases). Our result shows that in infinite domains, there are more general types of quantifiers that support these entailments.
Keywords generalized quantifier  monotonicity  scope  dominance
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DOI 10.1007/s10849-005-4960-6
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