 Since Mirimanoff, Finsler and others, logicians have studied universes of set theory where circular sets exist. However, it is only since the early Eighties that a genuine mathematics of non-well-founded sets (see |   set theory: non-wellfounded)  is being developed. Using the axiom AFA of anti-foundation, direct self-reference is allowed in set theory, and there exist plenty of sets solving general self-referential equations (AFA was introduced by Forti and Honsell in 1983; for systematic development and history, see Aczel 1988). In particular, non-wellfounded sets are applied to the analysis of the paradoxes, to the semantics of natural languages and to theoretical computer science (see Barwise and Etchemendy 1984, Barwise and Moss 1996).