[FOM] induction and reducibility
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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