FOM: iterative conception of set
neilt at mercutio.cohums.ohio-state.edu
Fri Feb 27 13:58:26 EST 1998
M. Randall Holmes wrote
> The notion "set of ZFC" can be coded into higher order logic as
> "isomorphism class of (pointed) well-founded extensional relations".
> This notion is purely logical if the notion of set (class) as the
> extension of a concept is taken as purely logical. It is a third-order
> concept in higher order logic.
> To get this notion to satisfy the axioms of ZFC, one needs to suppose
> that one has "enough" objects. Nothing else is needed. One
> doesn't even need any concept of iterative construction, though this
> concept is certainly intuitively appealing.
What would this establish for one who thinks that second order logic is just set theory in disguise?
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