FOM: iterative conception of set

Randall Holmes holmes at
Fri Feb 27 15:51:06 EST 1998

I think that second-order logic is a kind of set theory myself.  But
second order logic is typed set theory; one is not considering sets
of sets.  I'm not eliminating sets; I'm eliminating the unlimited
iteration of set construction in ZFC.

The context in which this arises is the simulation of Zermelo-style
set theory in NFU, where induction/recursion along the membership
relation is forbidden.  It turns out that the Zermelo universe
is nonetheless perfectly easy to discuss via the interpretation
in isomorphism types.  


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