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If $A$ is any upper bound for the arithmetic degrees then $0^{(\omega)}$ is recursive in $A^{\prime\prime}$. Enderton and Putnam proved that there upper bounds where $A$ with $A^{\prime\prime}=0^{(\omega)}$
If $A$ is any upper bound for the arithmetic degrees then $0^{(\omega)}$ is recursive in $A^{\prime\prime}$. Enderton and Putnam proved that there upper bounds where $A$ with $A^{\prime\prime}=0^{(\omega)}$