Addendum to "The Truth is Never Simple"

The present note outlines an answer to a question listed as open in our recent survey article [1], familiarity with which is assumed. Let Γ be the class of all X ⊆ ω such that X is reducible to for some some arithmetical and some positive with Y ⊆ p ( Y ) for all Y . A.1. Theorem. is a complete set of class Γ. A.2. Corollary, (a) is - in-a - - parameter . (b) (i) Every set - in-a - - parameter is reducible to . (ii) Every set - in-a - - parameter is reducible to . Remarks. A.1 answers 7.3 of [1]. A.2 says as much as can be said about in terms of the coarse classifications of the analytical hierarchy. A.2 follows from A.1 by general methods and results in the theory of inductive definitions (having nothing specifically to do with truth), and its proof will be omitted. Proof of A.1. We omit subscripts vF. Upper Bound . Define