Scope dominance with upward monotone quantifiers

Abstract
We give a complete characterization of the class of upward monotone generalized quantifiers Q1 and Q2 over countable domains that satisfy the scheme Q1 x Q2 y φ → Q2 y Q1 x φ. This generalizes the characterization of such quantifiers over finite domains, according to which the scheme holds iff Q1 is ∃ or Q2 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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References found in this work BETA
Thomas Ede Zimmermann (1993). Scopeless Quantifiers and Operators. Journal of Philosophical Logic 22 (5):545 - 561.
Dag Westerståhl (1996). Self-Commuting Quantifiers. Journal of Symbolic Logic 61 (1):212-224.

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