[FOM] Why would one prefer ZFC to ZC?
Jeremy Bem
jeremy1 at gmail.com
Tue Jan 26 17:09:27 EST 2010
Hi!
In a recent thread entitled "Mac Lane set theory", I tried to explain
why I tentatively prefer ZC to ZFC (as a foundation for mathematics).
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.
Arguably, the existence of such a construction makes ZC qualitatively
more justified than ZFC. As an informal consistency proof, it is an
application of ordinary model theory, rather than a unique argument
involving an exotic "union over all ordinals" and a class-sized
"model".
I don't claim that this argument is overwhelmingly compelling, but it
is an argument. Why would someone prefer ZFC?
-Jeremy
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