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:: <math>\{X \,|\, \{x \,|\, \mbox{x is a boy}\} \subseteq X \}</math>
This treatment of quantifiers has been essential in achieving a [[compositionality|compositional]] [[semantics]] for sentences containing quantifiers.<ref> [[Richard Montague|Montague, Richard]]: 1974, '[http://www.blackwellpublishing.com/content/BPL_Images/Content_store/Sample_chapter/9780631215417/Portner.pdf The proper treatment of quantification in English]',
in R. Montague, Formal Philosophy, ed. by R. Thomason (New Haven). </ref><ref>[[Jon Barwise|Barwise, Jon]] and Robin Cooper. 1981. Generalized quantifiers and natural language. ''Linguistics and Philosophy'' 4: 159-219.</ref>
==Type theory==
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