  Kremer's proof exploits an intimate relationship between circular definitions understood revision-theoretically and circular definitions understood as inductive definitions: the theory of inductive definitions has been quite well understood for some time. In particular, Kremer proves that every inductively defined concept can be revision-theoretically defined. The expressive power and other aspects of the revision-theoretic treatment of circular definitions is the topic of much interesting work: see Welch 2001, Löwe 2001, Löwe and Welch 2001, and Kühnberger et al. 2005.