  Aczel’s work became influential for two research areas.  He visited Stanford in 1985, where Jon Barwise was director of the Center for the Study of Language and Information (and this author was a post-doc there).  Barwise recognized the value of the work, partly because he had similar problems with Foundation in his own work on situation semantics, and partly because he saw in the work an appealing conception of set that was at odds with the iterative conception that had been received wisdom for him and practically everyone else raised in the mainstream tradition of mathematical   logic.[5]  He thought that non-wellfounded sets should be called by a name that reflected the change in conception, and he proposed calling them hypersets in parallel to the hyperreal numbers of non-standard analysis.  This terminology has for the most part not stuck, but it is not completely outdated, either.  In this entry, we’ll use both terms interchangeably.