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

On 5/29/24 10:36 PM, olcott wrote:

On 5/29/2024 9:25 PM, Richard Damon wrote:

On 5/29/24 9:55 PM, olcott wrote:

When the category is examined all at once then there is no need
to look at each individual element.

>
So, which one or ones gave the correct answer for their input?
>

 *Formalizing the Linz Proof structure*
∃H  ∈ Turing_Machines
∀x  ∈ *Turing_Machines_Descriptions*
∀y  ∈ Finite_Strings
such that H(x,y) = Halts(x,y)
 When we formalize it that way then some simulating halt deciders
get the correct answer.
 *Everyone else implicitly assumes this incorrect formalization*
∃H  ∈ Turing_Machines
∀x  ∈ *Turing_Machines*
∀y  ∈ Finite_Strings
such that H(x,y) = Halts(x,y)
 

Nope.
You just don't understand the meaning of a "Description" in the problem.
H is asked about a specific Turing Machine, by passing it a complete representation of that machine in symbolic form.
Just as for most problems, other than those which happen to be defined in terms of the same symbol set as the Turing Machie uses.