满足Zilber剖分的强极小理论的递归谱
Recursive spectra of strongly minimal theories satisfying the Zilber trichotomy
摘要：
我们猜想，对于满足Zilber三分性的有限签名中的强极小理论T，T的递归谱只有三种可能：T的所有可数模型都是递归可表示的;它们都不是递归可表示的;或者只有T的零维模型是递归可表示的.我们证明了这一猜想分解（以前，平凡）的理论和模群。该猜想也通过已知的领域的结果。该猜想仍然开放的有限覆盖的群体和领域。
英文摘要：
We conjecture that for a strongly minimal theory T in a finite signature satisfying the Zilber Trichotomy, there are only three possibilities for the recursive spectrum of T: all countable models of T are recursively presentable; none of them are recursively presentable; or only the zero-dimensional model of T is recursively presentable. We prove this conjecture for disintegrated (formerly, trivial) theories and for modular groups. The conjecture also holds via known results for fields. The conjecture remains open for finite covers of groups and fields.
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