Motivated by ideas from the study of abstract data types, the authors show how to interpret non-well-founded sets as fixed points of continuous transformations of an initial continuous algebra. They consider a preordered structure closely related to the set HF of well-founded, hereditarily finite sets. By taking its ideal completion, the authors obtain an initial continuous algebra in which they are able to solve all of the usual systems of equations that characterize hereditarily finite, non-well-founded sets. In this way, they are able to obtain a structure which is isomorphic to HF/sub 1/, the non-well-founded analog to HF.
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机译：作者展示了从抽象数据类型研究中的思想，展示了如何将非良好成立的集解释为初始连续代数的连续变换的固定点。他们认为预订结构与良好成立的默许有限套装的集合HF密切相关。通过实现理想的完成，作者获得了初始连续代数，它们能够解决特征有限，非良好成立的集合的所有常规方程式。以这种方式，它们能够获得对HF / SUB 1的同性恋的结构，非良好地创建的类似物到HF。
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