Re: non-Archimedean models of Euclidean geometry?
- From: David C. Ullrich <dullrich@xxxxxxxxxxx>
- Date: Tue, 10 Mar 2009 06:33:35 -0500
On Mon, 09 Mar 2009 15:10:38 +0200, Aatu Koskensilta
<aatu.koskensilta@xxxxxx> wrote:
Gc <Gcut667@xxxxxxxxxxx> writes:
There are no non-archimedian models for this theory. There is up to
isomorphism exactly one model for each infinite cardinal. That follows
from that the theory is complete.
No, it doesn't. Consider for example Presburger arithmetic.
I gave what seems to me to be a very simple counterexample,
the language with exactly one unary predicate P and the
theory being "there exist infinitely many x such that P(x)
and there exist infinitely many x such that ~P(x)"
(formalized in the obvious way as a collection of fol wffs).
It seems "clear" to me that this theory is complete, but
I have no idea how I'd prove it. Does it seem clearly
complete to you, and if so does it seem to you the
proof should be clear as well?
David C. Ullrich
"Understanding Godel isn't about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)
.
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