[FOM] Falsification of Platonism

Lucas Kruijswijk L.B.Kruijswijk at inter.nl.net
Sun Apr 25 18:52:31 EDT 2010

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?

We know that higher order logic and ZFC are not a conservative
extension of PA, but that is not the same as equiconsistency.

Furthermore, if it can be proven that PA and a more advanced systems
are equiconsistent, then adding a constructive omega rule to PA, which
uses the same logic as what was used to proof equiconsistency, to apply
the omega rule, then that modified PA system is much stronger, and the
systems that are proven to be equiconsistent are a conservative extension
of the modified PA sentence for PI0/2 sentences, I guess.


Lucas Kruijswijk

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