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Mar
25
awarded  Enthusiast
Feb
10
comment Cohesive sets with degree below some non-high 1-generic degrees?
No but this is not so difficult. Fix a functional $\Phi$, define $W$ by adding any string $\sigma$ such that for some $n$, $\varphi_n(n)\downarrow$ and $\Phi^\sigma(n) \ne \varphi_n(n)$. If $G$ is 1-generic and $G$ meets $W$ the $\Phi^G$ is not DNC, if $G$ avoids $W$ (say at $\sigma$) then $\Phi^G$ cannot be total (otherwise build a computable DNC by looking at convergences compatible with $\sigma$).
Feb
9
answered Cohesive sets with degree below some non-high 1-generic degrees?
Aug
14
answered Completeness, easiest, hardest problems
Aug
10
awarded  Supporter
Aug
10
awarded  Teacher
Aug
10
answered Differentiability of computable functions