Re: Request for clarification of what is a non first-order definable set.
- From: David C. Ullrich <ullrich@xxxxxxxxxxxxxxxx>
- Date: Sun, 28 Jan 2007 09:42:26 -0600
On 27 Jan 2007 15:59:52 -0800, "Scott" <ToaTerra@xxxxxxxxx> wrote:
On Jan 25, 9:42 am, G. Frege <nomail@invalid> wrote:
"It's common knowledge that it is n o t the case that for every
predicate p(x) there is a set {x : p(x)}. (-->Russell's Paradox)
Hence I think that the reviewer read your claim "backwards". I guess
he had in mind the claim "For every set s there is a predicate p(x)
such that s = {x : p(x)}", since this claim is much more reasonable
than your original one. But, as it turns out, it's false too, since
"there are sets which are not first-order definable." (See other posts
in this thread.)
That is correct. Now I'm trying to understand (or see) such a set.
You're not going to see an _explicit_ example. If I can tell you
exactly what set S I'm talking about I've _defined_ S, meaning
I've said what the elements of S are, meaning I've specified a
p such that S = {x : p(x)}.
************************
David C. Ullrich
.
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