The degrees of categorical theories with recursive models
Uri Andrews · Proceedings of the American Mathematical Society · 2013
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.