We say that a theory T satisfies arithmetic-is-recursive if any X′-computable model of T has an X-computable copy; that is, the models of T satisfy a sort of jump inversion. We give an example of a theory satisfying arithmetic-is-recursive non-trivially and prove that the theories satisfying arithmetic-is-recursive on a cone are exactly those theories with countably many ω-back-and-forth types.

中文翻译：

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锥上的“算术递归”属性

我们说一个理论吨满足算术递归（如果有）X'- 可计算模型吨有一个X- 可计算的副本；也就是说，模型吨满足一种跳跃反转。我们举一个非平凡的满足算术递归的理论的例子，并证明满足锥上算术递归的理论正是那些具有可数多的理论ω- 来回类型。