[FOM] Potential and Actual Infinity

[Joseph Shipman]

To define epsilon-zero, no infinity is necessary, but try proving as rigorously as you can that it is in fact well-ordered! Specify clearly the axiomatic system in which you expect to be able to prove this.

-- JS

Sent from my iPhone

> On Mar 13, 2015, at 8:14 PM, sambin at math.unipd.it wrote:
> 
> 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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