Journal of Symbolic Logic 58 (1):314-325 (1993)

Abstract
Recent work in natural language semantics leads to some new observations on generalized quantifiers. In § 1 we show that English quantifiers of type $ $ are booleanly generated by their generalized universal and generalized existential members. These two classes also constitute the sortally reducible members of this type. Section 2 presents our main result--the Generalized Prefix Theorem (GPT). This theorem characterizes the conditions under which formulas of the form Q1x 1⋯ Qnx nRx 1⋯ xn and q1x 1⋯ qnx nRx 1⋯ xn are logically equivalent for arbitrary generalized quantifiers Qi, qi. GPT generalizes, perhaps in an unexpectedly strong form, the Linear Prefix Theorem (appropriately modified) of Keisler & Walkoe (1973)
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DOI 10.2307/2275339
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References found in this work BETA

Generalized Quantifiers and Natural Language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.
Quantifiers in Formal and Natural Languages.Dag Westerståhl - 1989 - In Dov Gabbay & Franz Guenthner (eds.), Handbook of Philosophical Logic. Kluwer Academic Publishers. pp. 1--131.
Beyond the Frege Boundary.Edward L. Keenan - 1992 - Linguistics and Philosophy 15 (2):199-221.
Polyadic Quantifiers.Johan Benthem - 1989 - Linguistics and Philosophy 12 (4):437 - 464.

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Split Intensionality: A New Scope Theory of de Re and de Dicto.Ezra Keshet - 2010 - Linguistics and Philosophy 33 (4):251-283.
In Situ Interpretation Without Type Mismatches.Edward L. Keenan - 2016 - Journal of Semantics 33 (1):87-106.
Scope Dominance with Upward Monotone Quantifiers.Alon Altman, Ya'Acov Peterzil & Yoad Winter - 2005 - Journal of Logic, Language and Information 14 (4):445-455.

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