# [FOM] iterative conception/cumulative hierarchy

T.Forster at dpmms.cam.ac.uk T.Forster at dpmms.cam.ac.uk
Sat Feb 25 15:42:09 EST 2012

Not really: what is needed is that sets be constructed recursively. It is
not sufficiently widely appreciated that this does *not* imply that $\in$
should be wellfounded. See my article in Review symbolic logic vol 1 #1
page 1!

On Feb 25 2012, Hendrik Boom wrote:

>What's really needed is for the sets all to be well-founded in the
>membership relation.  Except you probably can't say that within the set
>theory, because well-founded is one of these intuitively clear slippery
>concepts that goes awry when things become too general.
>
>Ordinally-indexed stages is a formal way to approximate this concept.
>
>