# Are all complete finitely axiomatizable first order theories $\aleph_0$-categorical?

Suppose $T$ is a complete first order theory with a finite axiomatization. Must $T$ be $\aleph_0$-categorical? If not are there any simple examples of finitely axiomatized complete first order theories which are not $\aleph_0$-categorical?

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From a quick look at David Marker's model theory textbook (GTM 217), the answer is no. In exercise 2.5.16 he gives a finitely axiomatizable theory that is $\aleph_1$-categorical and without finite models (thus complete), but not $\aleph_0$-categorical. The theory looks to be anything but simple, however. I hope that someone can chime in with a nicer example. –  Garrett Ervin Sep 28 '13 at 4:08
The answer is no: for a simple example, take $Th(\mathbb Z,<)$. The axioms are:
• $<$ defines a linear order;