I have some error: from the below it follows that if the formal system found is distinct from the original one then it’s provable that the input algorithm does not halt (if it halts, it’s provable that it halts in Peano arithmetic)…

read moreA statement equivalent to First Incompleteness theorem There are theorems that can be neither proved nor disproved in a given formal system (containing arithmetic). This theorem makes people sad: There are “problems” that cannot be solved. But God teaches me that there…

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