no, because you can build an algorithm that fools the algorithm that solves the generic halting problem. I wrote a "proof" of that in my blog [1]
> So you can remove the ones that do not halt by inspecting them one by one and developing a specific algorithm for each one that determines if it halts or not.
Is impossible. You can’t, in general, inspect Turing machines one-by-one to determine if they halt.