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I'd like to understand the proof that if $K$ is an infinite field the theory of $K$ is $\aleph_1$-categorical, then $K$ is algebraically closed--but I'm having trouble finding it in the literature. Any ideas where I can find the appropriate paper(s)?

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This is called Macintyre's Theorem. In fact, the following are equivalent for infinite fields:

  1. $K$ is algebraically closed
  2. $\text{Th}(K)$ is $\aleph_1$-categorical
  3. $K$ is totally transcendental
  4. $\text{Th}(K)$ has quantifier elimination

The original paper is:

Macintyre, Angus, On $\omega_1$-categorical theories of fields. Fund. Math. 71 (1971), no. 1, 1–25.

It also appears as Theorem 3.1 in Stable Groups by Poizat.

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    Thanks. I have a copy of Marker, so the last bit shouldn't be a problem.2012-04-26