A Turing machine for which halting is outside ZFC If, given Turing machine T, "T halts" or "T doesn't halt" could be derived from axioms of ZFC, halting problem would be in R. As it isn't, there must exist a Turing machine for which truth or falsehood of halting is independent of ZFC.
I want to see it. Is such machine known?

Let $T$ be the Turing machine which looks for a proof of a contradiction in ZFC. If ZFC is consistent, then whether or not $T$ halts will be independent of ZFC. (Indeed, if not, then this would contradict Gödel's incompleteness theorem!)
