[FOM] Countable sets with impredicative definitions

Nik Weaver nweaver at math.wustl.edu
Sun Nov 21 13:38:51 EST 2010

Dana Scott wrote:

> The set of formulae of second-order arithmetic is countable.
> what about the two-element set {T, F} consisting of the true sentences
> and the false sentences.  Anything wrong with this?

That's right.  Or you could say: the set {n: A_n is true} where
(A_n) is some standard enumeration of the sentences of second order
arithmetic.  This example is discussed on page 2 of the survey paper
I mentioned in my last message.


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