... the set of sets of entities which have a non-null intersection with the set of students: {X Í A | X _ [student']M,g.¹ 0} and every student denotes the set of sets of entities of which the set of students is a subset: {X Í A | [student']M,g.Í X} Every is translated directly into every' rather than a complex expression using lambda. More generally, each quantifier is associated with a function which assigns to each subset [N]M,g. of A, a set of subsets of A having a particular property. This gives the following definitions for every and some: [every']M,g. is that function which assigns to each [N]M,g.Í A, the set of all sets {X Í A | [N]M,g. Í X}. [some']M,g. is that function which assigns to each [N]M,g.Í A, the set of all sets {X Í A | X _ [N]M,g. ¹ 0}. The proposition expressed by Every student laughed ...

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