i-Rigid Pairs. The idea is to use as an intermediary a two-sorted language with a special category of terms which are stipulated to behave, in modal contexts, the way Semi-Rigid Pairs requires all terms for relations to behave. Let me sketch the strategy in a bit more detail. We start with a languageLACT with the modal operators ,^ and ACT, singular and plural quantifiers and variables, a predicate C taking one plural argument, a distinguished plural term I, and the ordered-pair-forming functor '〈*, *〉'. We will recursively specify a translation function from LACT into L, the modal-operator-free sublanguage of LACT. Our translation will use sentences of a third language LW as intermedi26 aries. LW is like L except that (i) its plural terms can optionally be underlined, in which case we will call them "world terms", and (ii) it contains an operator 'at' that takes a world term W and a sentence φ to make a sentence pat W (φ)q. The translation from LACT to LW is straightforward: wherever we have '^φ', we substitute '∃V(CV∧at Vφ)', where V is some new world variable; wherever we have 'φ', we substitute '∀V(CV → at V (φ))'; wherever we have 'ACTφ', we substitute 'at I (φ)'. The central task in translating from LW to L is to eliminate all occurrences of the 'At' operator. To do so, we replace each formula of the form 'at Rφ(t1, . . . , tn)' with φ(α1, . . . , αn), where αi is pR(ti)q when ti is a singular term or a non-underlined plural term, and αi is pti ◦ R−1q when ti is an world term. As usual, we treat sentences involving complex terms like 'R(a)' and 'S◦R−1' in Russellian fashion, as abbreviations for quantified sentences of LW: '(S ◦ R−1)ab', for example, abbreviates '∃Q(∀xy(Qxy ↔ ∃z(Rzx ∧ Szy)) ∧ Qab)'. By repeatedly applying this rule, we can turn each sentence of LW into an 'at'-free sentence. Finally, we can translate this sentence into L simply by dropping all the underlines. Here is an example of the machinery at work. Suppose our original sentence φ of 