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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