Is the following language recursively enumerable?
I'll provide some hint. Try building a reduction $\overline{L_{acc}} \leq L$
changing your argument as follows:

... where $&lt;M_w&gt;$ is a TM that, on an input $x$ it performs:


Run $M$ on $w$ for $|x|$ steps
If $M$ rejected within $|x|$ steps ...
If $M$ accepted within $|x|$ steps ...
If $M$ did not halt within $|x|$ steps ...


When $M$ does not accept $w$, you want the above to diverge only on finitely many $x$s.

When $M$ accepts $w$, you want the above to diverge on infinitely many $x$s.



Alternatively, you can try to exploit the Rice-Shapiro theorem.