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Topic: Matheology § 213
Replies: 3   Last Post: Feb 9, 2013 6:44 PM

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Posts: 18,076
Registered: 1/29/05
Matheology § 213
Posted: Feb 9, 2013 6:59 AM
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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 well-ordering 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)]

Regards, WM

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