Since the conventional HP only mentions a specific halting problem, which is
often believed to be an invalid proof.
See https://groups.google.com/g/comp.theory/c/RO9Z9eCabeE/m/Ka8-xS2rdEEJ

I hereby claims the General Undecidable Axiom(2021 WIJ):
+--------------------------------------------------------------------------------+
| No TM U can decide the property of a TM P if that property can be defied by TM P. |
+--------------------------------------------------------------------------------+

// Example1:
// [Ret] true: f prints 'Y'
// false: f does not print 'Y'
bool U(Func f);

void P() {
if(U(P)) {
printf("b");
} else {
printf("Y");
}
} //---

// Example2:
// [Ret] true: f is a "pathological self-reference" function
// false: otherwise
bool U(Func f);

void P() {
if(U(P)) {
return;
} else {
P(); // if "pathological self-reference" is so defined, whatever.
}
};

--
Copyright 2021 WIJ

On Sunday, 11 July 2021 at 01:23:51 UTC+8, wij wrote:
> Since the conventional HP only mentions a specific halting problem, which is
> often believed to be an invalid proof.
> See https://groups.google.com/g/comp.theory/c/RO9Z9eCabeE/m/Ka8-xS2rdEEJ
>
> I hereby claims the General Undecidable Axiom(2021 WIJ):
> +--------------------------------------------------------------------------------+
> | No TM U can decide the property of a TM P if that property can be defied by TM P. |
> +--------------------------------------------------------------------------------+
>
> // Example1:
> // [Ret] true: f prints 'Y'
> // false: f does not print 'Y'
> bool U(Func f);
>
> void P() {
> if(U(P)) {
> printf("b");
> } else {
> printf("Y");
> }
> }
> //---
>
> // Example2:
> // [Ret] true: f is a "pathological self-reference" function
> // false: otherwise
> bool U(Func f);
>
> void P() {
> if(U(P)) {
> return;
> } else {
> P(); // if "pathological self-reference" is so defined, whatever.
> }
> };
>
> --
> Copyright 2021 WIJ

The construct of P (proof of General Undecidable Axiom) is 100% correct,
intuitive and above all, REPRODUCIBLE, VERIFIABLE.

// [Ret] true: f has the (dynamic)property Q
// false: otherwise
bool U(Func f);

void P() {
if(U(P)) {
// do whatever Q defines false
} else {
// do whatever Q defines
}
};

Note: I would like to acknowledge Olcott tirelessly refuted various conventional
HP proofs over these years. So I need not to do the same work again, though not necessary.

--
Copyright 2021 WIJ