[FOM] Falsification of Platonism
rgheck at brown.edu
Mon Apr 26 08:43:49 EDT 2010
On 04/25/2010 06:52 PM, Lucas Kruijswijk wrote:
> Daniel Méhkeri wrote:
>> The example of a contradiction in ZFC is different, because there
>> is no corresponding equiconsistent constructive system.
> As far I know, the equiconsistency between PA and ZFC is still an
> open question. Or am I wrong?
ZFC proves Con(PA), so ZFC and PA are equiconsistent (in the only sense
I understand) only if both are inconsistent. And one does not nearly
need to go to ZFC. Even second-order PA with induction limited to Pi-1-1
formulas proves Con(PA). This is because truth for a first-order
language is Pi-1-1, so if you have induction for such formulas you can
carry out the "trivial" semantic proof of consistency.
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