Re: D correctly simulated by H cannot possibly halt --- templates and infinite sets

Am Sat, 01 Jun 2024 14:55:40 -0500 schrieb olcott:

On 6/1/2024 1:56 PM, joes wrote:

Am Sat, 01 Jun 2024 09:52:54 -0500 schrieb olcott:

On 6/1/2024 3:20 AM, Mikko wrote:

On 2024-05-31 15:44:22 +0000, olcott said:

On 5/31/2024 8:10 AM, Mikko wrote:

On 2024-05-28 16:16:48 +0000, olcott said:
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Your ∃H declares H as a new symbol for a specific Turing machine.
Therefore everything that follows refers to that specific Turing

machine.

There may be others that could be discussed the same way but they

aren't.

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      The domain of this problem is to be taken as the set of all
      Turing machines and all w; that is, we are looking for a
      single Turing machine that, given the description of an
      arbitrary M and w, will predict whether or not the
      computation of M applied to w will halt.

Note the words "a single Turing machine".

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I misunderstood this, too, but we want a single machine that solves the
problem on its own, not multiple that each solve parts. There could be
many such machines.
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∃H ∈ Turing_Machines is fulfilled when there are one or more machines
that independently solve the halting problem.

Exactly. If there are any such machines, every single one must solve it
on its own.