On a Representation of Hyperarithmetical Predicates

In Aslyan [1] the representability of arithmetical predicates by means of general form recursive equations is proved. Here we show that arbitrary hyperarithmetical predicate (, …, ) is representable by the system of recursive equations. On the other hand it is shown that the class of hyperarithmetical predicates is the largest class of predicates representable by means of recursive equations. This presents a new characterisation of hyperarithmetical sets “from outside”, where, characteristic functions of hyperarithmetical sets are described as a unique solutions of G.F.R.E