FOM: beautiful from the point of view of a classical analyst

[friedman@math.ohio-state.edu]

Reply to ELENA NOGINA <enogina at alpha.lehman.cuny.edu>.
> 
> Is not   
> Specker's first example of a convergent, computable sequence of rationals 
> which does not converge computably, hence its limit  is not computable
> (Nicht konstruktiv beweisbare S"atze der Analysis, J. Symbolic Logic
> 14(1949), 145-158) 
> defined in a beautiful way? 
> 
> Elena Nogina (Artemov)
>  
> 
Without looking, I assume that it uses a partial recursive enumeration of the 
partial recursive functions, or an r.e. enumeration of the r.e. sets, etc. This 
might be beautiful if the enumeration used is beautiful. However, there is no 
suitably beautiful enumerations known. 

If Specker doesn't rely on such enumerations, then it would be nice if you 
could sketch the construction here on the FOM e-mail list, so we can examine 
the beauty (from the point of view of the classical analyst).


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