[FOM] J_2

Nik Weaver nweaver at math.wustl.edu
Sat Mar 23 02:02:08 EDT 2013

Arnon Avron wrote:

> I am afraid that saying that J_2 is just as concrete as the natural 
> numbers is an exaggeration ... Are the membership relation and the 
> equality relations on J_2 decidable, and if so - in what sense?


I take your point.  Of course, in that sense J_2 is not as "concrete"
as omega.  I merely meant that the elements of J_2 can be represented
in just as concrete a form (say, as finite strings) as the natural
numbers.  As for membership and equality, these are decidable by
computations of countable length, so I still think it is fair to
say that anyone who accepts omega as a completed object should not
have any philosophical objection to accepting J_2.

Naturally I am interested in your simplifications of my paper.
Could you tell me more (off-list perhaps)?


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