Re: non-Archimedean models of Euclidean geometry?

On Tue, 10 Mar 2009 14:39:29 +0200, Aatu Koskensilta
<aatu.koskensilta@xxxxxx> wrote:

Aatu Koskensilta <aatu.koskensilta@xxxxxx> writes:

Come to think of it, this basically amounts to a trivial quantifier
elimination.

Or, in the slapping-of-forehead department, we may simply observe the
theory is countably categorical.

Here's a curious fact: That sentence suffices to answer my
question completely and very simply even though I
haven't yet found out _exactly_ what "countably
categorical" means!

Glancing at

http://en.wikipedia.org/wiki/Vaught%27s_test

I conjecture that "countably categorical" means
either

(i) any two countable models are isomorphic

or

(ii) any two countable models are elementarily
equivalent.

The present theory obviously satisfies (i). And
then I slap my forehead as well: If the theory
were incomplete then L-S would show that
T + phi and T+ ~phi both had a countable
model for some phi, contradicting the
countable categoricity.

Duh.

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.)
.