[FOM] Potential and Actual Infinity

[sambin at math.unipd.it]

Quoting "Timothy Y. Chow" <tchow at alum.mit.edu>:

> Arnon Avron also claimed that potential infinity was all that was  
> needed to prove the consistency of PA, but unless I missed  
> something, has not responded to my request for a more formal  
> justification of this claim.
>
> Tim

Gerhard Gentzen in the 30s proved that PA is consistent using  
induction up to the famous ordinal epsilon-zero. To define such an  
ordinal, no actual infinity is necessary.

Giovanni Sambin

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