FOM: Re: [HM] On one feature of Cantor's Diagonal Method

[Roger Cooke]

You might be interested in some of Nikolai Nikolaevich Luzin's
speculations on the CDM.  He argued that the hypothesis of an enumeration
fails to consider  surjections of the integers onto the
reals that might "exist" in a purely abstract sense, that the argument  
rules out
only "effective enumerations" of the reals.  I don't think he ever
published them, but they are in some of his notes, which you may be able
to find in the Academy Archives.  I can give you exact references (at
least as of 1988, when I was there---the fond numbers were changing then,
and may be completely different now).  The Luzin fond number is 606.

Best wishes,

Roger Cooke