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Recursion Theory by Liang Yu, Chi Tat Chong

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8 The construction of image-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 image-sets. The reader is referred to [47] and [106] for more on this subject. ...

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