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.
}
};
------------------------
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
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