[FOM] Thoughts on CH 2

Arnon Avron aa at tau.ac.il
Sun Aug 17 02:22:48 EDT 2014

Quoting joeshipman at aol.com:

"No detailed structure theory" is such a cop-out.

They simply don't like the axiom and so give a vague standard that is 
neither described precisely, nor demonstrated for alternative axioms.

Several times on this forum, I have challenged set theorists to explain 
what is wrong with the real-valued-measure axiom and I have never gotten 
a response. From the RVM axiom, all kinds of things can be proven about 
sets of reals, in fact very little of interest is left undecided by this 
axiom. It also has the consistency strength of a large cardinal axiom 
(measurable cardinal). What's not to like?"

I am not an official set theorist, so I suppose my opinion does
not count. Still I would like to point out two small problems that
I see with this axiom:

A) It is no more definite mathematical proposition than CH (personally
   I find it totally meaningless).

B) Even if it is meaningful, I see no convincing *mathematical* argument
   for its truth.

     Concerning the second point, I know that I am out-dated and
   old-fashioned, but for me the truth of mathematical assertion is not
   determined by voting or rating, but only by a full, rigorous
   mathematical proof.

Arnon Avron

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