[FOM] Why would one prefer ZFC to ZC?
Monroe Eskew
meskew at math.uci.edu
Tue Jan 26 23:20:59 EST 2010
You need the axiom of replacement to prove the existence of
V_{\omega*2}. So your argument requires the acceptance of ZFC in the
background.
It's similar to saying the following: If \kappa is the least
inaccessible, V{\kappa} is a model of ZFC. Hence there is a set model
of ZFC without inaccessibles. Thus we don't need to believe in
inaccessibles.
Godel's incompleteness theorem sheds a lot of light here.
Monroe
On Tue, Jan 26, 2010 at 2:09 PM, Jeremy Bem <jeremy1 at gmail.com> wrote:
> To summarize that argument: whatever role the "Von Neumann universe"
> plays in justifying ZFC, can be played for ZC by "V_{omega+omega}".
> But whereas the former construction is said to yield a proper class,
> the latter appears to be a set -- making it a model in the ordinary
> sense of first-order logic.
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