The automorphism group and definability of the jump operator in the $$\omega $$ ω -enumeration degrees

Archive for Mathematical Logic 60 (7):909-925 (2021)
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Abstract

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

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