8 The construction of 
-sets
As seen in the previous chapters, inductive definition plays a key role in hyperarithmetic theory. In fact Gandy (see [106]) held the view that inductive definition rather than computation constituted the core characteristic of any generalized recursion theory. Admissible set theory (Chapter 3) reinforces the line of thought. Here we discuss inductive definition in greater detail and present some applications of this notion to the construction of 
-sets. The reader is referred to [47] and [106] for more on this subject. ...
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