• Korean Journal of Logic
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• v.19 no.1
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• pp.83-106
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• 2016

We compare the approaches to natural numbers and the induction principles in Frege's Grundgesetze and in systems thereafter. We start with an illustration of Frege's approach and then explain the use of induction principles in Zermelo-Fraenkel set theory and in modern type theories such as Calculus of Inductive Constructions. A comparison among the different approaches to induction principles is also given by analyzing them in respect of predicativity and impredicativity.