FOM: Re:GII/clarification

Harvey Friedman friedman at
Thu Jan 8 22:06:23 EST 1998

This is a reply to Walter Felscher 4:01PM 1/8/98.

Perhaps instead of AC and CH, I should have said WO and CH, where WO = well
ordering principle = every set is well ordered. E.g.,

"Around 1895, when Cantor became convinced that the Well-Ordering Principle
was a theorem rather than a law of thought, he dilligently sought a proof.
By 1897 he believed that he had found one. Yet he remained somewhat ill at
ease with the proof, since he later refused permission to publish it."

This is from Gregory H. Moore, Zermelo's Axiom of Choice: its origins,
development, and influence, 1982, Springer-Verlag.

Of course, WO is demonstrably equivalent to AC within ZF and weak fragments
thereof. However, you are correct in stating that Cantor never formulated
AC directly.

Your Infallible Historian (?)

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