Abstract
We show that even for categorical theories, recursiveness of the models guarantees no information regarding the complexity of the theory. In particular, we show that every tt-degree reducible to 0 ( ω ) 0^{(\omega )} contains both ℵ 1 \aleph _1 -categorical and ℵ 0 \aleph _0 -categorical theories in finite languages, all of whose countable models have recursive presentations.
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