[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.
[snip]
> 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.
Nik
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