[FOM] induction and reducibility

Thomas Forster T.Forster at dpmms.cam.ac.uk
Thu Oct 25 03:51:18 EDT 2007

I am interested to hear Robert's contribution - particularly the 
historical detail. However we mustn't infer from this any particular 
significance about reducibility.  The point is that reducibility functions 
as a set existence axiom, and - since we define the naturals inductively 
as the intersection of all *sets* containing 0 and closed under S - each 
time we prove the existence of a new *set* we obtain the use of another 
instance of the induction scheme.

So it's an instance of a perfectly general phenomenon, and not really a
specific fact about reducibility.

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