Abstract
Anil Gupta and Nuel Belnap's The Revision Theory of Truth presents revision theoretic systems of circular definitions. Part I of the present paper shows that the revision theories S# and S* are not axiomatis- able. Part II refines this result. Among other things, Part II shows that there is a strong relationship between revision theories and the theory of inductive definitions. This relationship is exploited to show that S# and S* (and all plausible revision theories of circular definitions) are of complexity at least Π^.
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