In the present paper, we show the first-order definability of the jump operator in the upper semi-lattice of the \(\omega \)-enumeration degrees. As a consequence, we derive the isomorphicity of the automorphism groups of the enumeration and the \(\omega \)-enumeration degrees.

中文翻译：

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$$ \ omega $$ω-枚举度的自同构群和跳跃算子的可定义性

在本文中，我们显示了\（\ omega \）-枚举度的上半格中跳跃算子的一阶可定义性。结果，我们得出了枚举和\（\ omega \）枚举度的同构群的同构性。