We look at various notions of a class of
definability operations that generalise inductive
operations, and are characterised as “revision
operations”. More particularly we: (i) characterise the revision theoretically
definable subsets of a countable acceptable
structure; (ii) show that the categorical truth set
of Belnap and Gupta’s theory of truth over
arithmetic using \emph{fully varied revision}
sequences yields a complete \Pi13 set of
integers; (iii) the set of \emph{stably categorical}
sentences using their revision operator ψ is
similarly \Pi13 and
which is complete in Gödel’s universe of constructible sets L;
(iv) give an alternative account of a theory of truth—realistic variance that simplifies full variance, whilst at the same time
arriving at Kripkean fixed points.