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Would you consider the Collatz conjecture as potentially undecidable? Because that one needs to be solved for BB(6) already: https://wiki.bbchallenge.org/wiki/

Would you consider the Collatz conjecture as potentially undecidable? Because that one needs to be solved for BB(6) already: https://wiki.bbchallenge.org/wiki/Antihydra https://wiki.bbchallenge.org/wiki/Antihydra Considering how we made basically no real progress on it mathematically in a whole generation, solving BB(6) within the next decades would be a miracle, and I would bet a lot against it. I can't see us EVER getting to BB(10), no matter how advanced humanity grows (and it would be meaninglessly large anyway). I think 765 is just a huge overestimation based on the fact that it is somewhat straightforward to construct.

Sniffnoy 2y ago
First off, it's not Collatz, it's a Collatz-like problem. But yes, I'd be very surprised if Collatz were actually undecideable, even if it's well beyond the reach of current mathematics. I agree with your statements about BB(10) and BB(6), but they just aren't very relevant. I agree those involve extremely difficult problems likely well beyond the reach of current mathematics, but I'd still be very surprised to find anything undecideable in there. There's a big difference between being truly undecideable and merely well beyond the reach of current mathematics! (Also, the current record for undecideability is 745, or 765.)