[FOM] Might there be no inaccessible cardinals?
pratt at cs.stanford.edu
Fri Nov 2 02:03:05 EDT 2007
I ran across an interesting paper by Jesus Mosterin titled "How set
theory impinges on logic" at
The following sentence caught my eye.
"In ZFC we can neither prove nor disprove the existence of inaccessible
Can anyone (Mosterin perhaps?--I don't have his email address) enlighten
me as to the meaning of "cannot" ("can neither") here?
In the case of "prove" there is no question: "cannot" means it is
impossible, since there are models of ZFC too small to include an
At first I assumed that he meant the same for "disprove." But I
couldn't immediately come up with an equally convincing argument, nor
was Google of much help.
Has this been shown? Or did Mosterin merely mean that we can't
*currently* disprove the existence of inaccessible cardinals?
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