FOM: Inconsistency JSHIPMAN at
Wed Nov 19 15:03:54 EST 1997

I am intrigued that Lou considers it quite possible that ZFC is inconsistent.
Three questions:
 1) Lou, do you feel the problem is with uncountable iteration of the power set
operation (that is,  would you accept V(alpha) for any countable ordinal alpha)?
If not, how high up do you feel comfortable going?  (It's a reasonable position
to say "omega+omega", this is equivalent to Zermelo's original set theory Z
before Replacement was propounded by Fraenkel.)  Do you use iteration of Power
freely in your own work, avoid it, or use it with explicit caveats?
 2) I would think that anyone who had a strong intuition that ZFC was
inconsistent would spend a lot of time trying to turn it into a proof, this
would be a bigger earthquake than Godel's.  So Lou probably has a "sneaking
suspicion" rather than a strong intuition.  Is anyone actually trying seriously
to show ZFC is inconsistent?  (I suspect those who are would not admit it.)
 3) Does anyone on FOM actually believe (subjective P > 0.5) that any standard
large cardinal axioms are inconsistent?  What about measurable cards?--J Shipman

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