Recent work in natural language semantics leads to some new observations on generalized quantifiers. In §1 we show that English quantifiers of type 〈1, 1〉 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 (Q1x1…QnxnRx1…xn and q1x1…qnxnRx1…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).