if you ask mathematicians whether ZFC + not Consistent(ZFC) is consistent, they will say “no, of course not!”
ZFC + not Consistent(ZFC)
I suspect than many people’s intuitive interpretation of “consistent” is ω-consistent, especially if they are not aware of the distinction.
I suspect than many people’s intuitive interpretation of “consistent” is ω-consistent, especially if they are not aware of the distinction.