在Kripke (1975), “Outline of a theory of truth”, 713页的脚注31中，他提到他的fixed point model construction可以被用于一种对impredicative substitutional quantification的modelling中。他写道：
Another application of the present techniques is to “impredicative” substitutional quantification, where the terms of the substitution class themselves contain substitutional quantifiers of the given type. (For example, a language containing substitutional quantifiers with arbitrary sentences of the language itself as substituends) It is impossible in general to introduce such quantifiers into classical languages without truth-value gaps. (Kripke 1975, p.713)
这听起来是一个很有趣的想法，尤其是把他的技术用于一种substitutional的对propositional quantifiers的阐释中。我很好奇有没有后续的文献执行了这个想法（我自己没有找到相关的文献），尤其是这种模型会造成的逻辑是什么？或者，大家对用这种技术来model substitutional propositional quantification有什么想法吗？