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Matheology § 213
Posted:
Feb 9, 2013 6:59 AM


Matheology § 213
Zermelo?s proof had not indicated how to determine the covering gamma uniquely, and yet one needed to be certain that gamma remained the same throughout the proof. How could one be sure? Moreover, even if such a covering gamma existed and could be defined, it was doubtful that one could use gamma in the way that Zermelo had; for the subsets M? of M were not defined in a unique way. Indeed, Lebesgue doubted that one would ever be able to state a general method for well ordering a given set. {{That was very wise. But it shows one fact above all: The possibility of a wellordering of the reals had been expected within reach at that time. Today its impossibility for the reals is well known. It is not admitted that this is contradicting Zermelo's proof because there cannot be a contradiction in a theory ZFC which stands for Zero Falsifying Contradictions.}} [Gregory H. Moore: "The Origins of Zermelos Axiomatization of Set Theory" (1978)] http://www.jstor.org/pss/30226178
Regards, WM



