Specifically, is it the case that (for $a,b\in\omega^\omega$) $a$ $\leq\_T$ $b$ implies $a$ $\leq\_c$ $b$?
I suspect it might be trivial, but not knowing much Recursion Theory, it's hard to see how it could.


Thank you in advance.



How does the Constructibility Degree of a real compare with its Turing Degree?
Yes, if $a\le\_T b$ then $a$ is first-order definable from $b$; in particular $a\in L(b)$ so $a\le\_c b$.


