4 ms·
> If other hypotheses (e.g. Goldbach, Riemann) turn out to have different results in differing axiom systems, that tells us something about those conjectures.
by openasocket 9y ago
> If other hypotheses (e.g. Goldbach, Riemann) turn out to have different results in differing axiom systems, that tells us something about those conjectures.
To be clear, you shouldn't (can't ?) have something like that Riemann is true under ZFC and false under ZFC + Continuity, because that would imply that ZFC + Continuity is inconsistent. You could have that Riemann is true under ZFC + Continuity but unprovable under ZFC, though.
- rocqua 9y agoIndeed, if we presume ZFC + Continuity to be consistent, then your situation cannot happen. However, it could be that ZFC + Continuity has Goldbach true, and ZFC + Forcing has goldbach false. I should say I recall reading that if the Riemand hypothesis is false, then it is provably so in ZFC, hence my inclusion of the Goldbach conjecture. [1, 2] [1] https://mathoverflow.net/questions/79685/can-the-riemann-hypothesis-be-undecidable https://mathoverflow.net/questions/79685/can-the-riemann-hyp... [2] https://www.youtube.com/watch?v=O4ndIDcDSGc&ab_channel=Numberphile https://www.youtube.com/watch?v=O4ndIDcDSGc&ab_channel=Numbe...