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Free structures pervade Mathematics: free monoids, free groups, the natural numbers are just the most obvious examples. These structures are characterised by a set of generators coupled with a generating process which allows to combine the generators with no constraints, roughly speaking. The generation process naturally yields an induction principle for the free structure: if a property holds for all the generators and it preserves the generating process, then the property holds for every element in the free structure. In this respect, induction can be thought of as an algebraic action of the free structure over some domain.
The talk aims at illustrating and exploring induction as an algebraic action, drawing a few, very preliminary consequences mainly through examples.
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