It is proved that for every countable structure and a computable successor ordinal α there is a countable structure which is ‐least among all countable structures such that is Σ‐definable in the αth jump . We also show that this result does not hold for the limit ordinal . Moreover, we prove that there is no countable structure with the degree spectrum for .

中文翻译：

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代数结构的跳跃反演和Σ可定义性

事实证明，对于每个可数结构和可计算的后继序数α，都有一个可数结构，该结构在所有可数结构中最少，因此可在第α个跳跃中定义Σ 。我们还表明，该结果不适用于极限序数。此外，我们证明了不存在可数的结构与程度谱的。