[FOM] The Gold Standard/correction

[Harvey Friedman]

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