Nature of undecidable halting

Am Thu, 16 May 2024 13:42:41 +0300 schrieb Mikko:

On 2024-05-15 15:06:26 +0000, olcott said:

I refer to transitioning through a specific state to indicate a
specific halt status value, for Turing Machines.

 
That does not satisfy the usual definition of "halt decider". However,
we could accept that as a solution to the halting problem if one could
prove that there is a Turing machine that can indicate halting or
non-halting that way for all computations.
 
However, it is possible to prove that every Turing machine that
indicates halting that way fails to indicate correctly at least some
computations.

Are these all of the liar paradox kind, such that one could easily
exclude them? Or do they form a more interesting class?

--
joes