Question: Let T be consistent, axiomatizable theory extending Q . Consider the set P ^ yes of ( code number of ) formulas that are provable

Let T be consistent, axiomatizable theory extending Q. Consider the set P^yes of (code number of) formulas that are provable in T, and the set P^no of (code numbers of) formulas that are disprovable in P. Show that there is no recursive set R such that P^yes is a subset of R while no element of R is an element of P^no.

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