[FOM] The Gold Standard/correction

Harvey Friedman friedman at math.ohio-state.edu
Thu Feb 23 22:02:53 EST 2006

On 2/23/06 4:44 PM, "Robert M. Solovay" <solovay at math.berkeley.edu> wrote:

Friedman wrote:

>> ZC looks like the closest formalization of general mathematical practice -
>> IF one insists on no coding.
>> Of course, some interesting stuff is missing...
> ZC is equiconsitent with ZC + Mostowski collapse + "Every set has a
> transitive closure". The latter theory is much more pleasant for the
> set-theorist to work in than ZC. {But of course not as nice as ZFC.]

I agree with this. Another way of saying this is to consider the equivalent
theory to Solovay's:

ZC + (forall x)(therexists an ordinal alpha)(x lies in V(alpha)).

Harvey Friedman

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