On 12/19/2012 2:14 PM, Bruno Marchal wrote:
I am trying to see if we can use the way that towers of theories are allowed by the incompleteness theorems...


This is studied in recursion theory. Turing shows that incompleteness continue to all effective transfinite tower, on the constructive ordinals.
Dear Bruno,

Yes, but we can see relative completeness between neighboring levels of the tower, no? Statement in Theory A that cannot be proven in A can be proven to be true in theory B that includes and extends beyond theory A, no?

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Onward!

Stephen


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