[FOM] Con(ZFC) is trivial
MartDowd at aol.com
MartDowd at aol.com
Tue Jan 22 12:09:18 EST 2013
In respnse to a recent posting of Vaugh Pratt, I have been reading over
Harvey's manuscript "A Divine Consistency Proof for Mathematics", to
see why he might have dismissed Con(ZFC) as not of much interest.
ZFC+"there exists a Ramsey cardinal" is interpretable in T_5. Ramsey
cardinals are strongly inaccessible. Thus, Con(ZFC) is a triviality.
Ramsey cardinals have not been strigently justified, and mathematicians
such as myself suspect that they never will be. Axioms which have been
stringently justified imply that the class of strongly inaccessible
cardinals is stationary. Thus, Con(ZFC) is a triviality even in this
much more limited setting.
I noted the following typos in Harvey's manuscript:
p.10, proof of lemma 1.1. Shouldn't the second sentence be
We want $\psi\leftrightarros\pi_1(\pi_2(\psi))E provable in S_2.
p.17, definition 3.1.ii, shouldn't this be
$X\in K$ iff $X\A\notin K$
p.17, theorem 3.1, second sentence; shouldn't this be
If $A\subseteq B$ and $A\in K$ then $B\in K$,
Si99 seens to be omitted from the references.
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