Hier eine Ankündigung von Jehanger und Angela Grami:
Cantor’s diagonal method has been the proof for the uncountable
infinite set of real numbers to be “larger” than the countable
infinite set of natural numbers. In the following work Cantor’s method
is refuted and it is proven that the cardinality of real numbers is
the same as the cardinality of natural numbers.
Contrary to Cantor’s method, this proof is constructive and estimates
directly the cardinality of the real numbers and compares it to the
natural numbers by constructing an injection to the prime numbers.
The work is written in German and shall be translated into English.
Until then the German version is the only source for the proof.
[J. Grami, A. Grami: "Die reellen Zahlen sind abzàhlbar." (2009)]