Goodstein’s theorem is a theorem about finite numbers that can be proven using infinite ordinals, and can’t be proven using just Peano Arithmetic. I take it that’s the kind of thing you’re asking about? Though I couldn’t tell you how useful that in turn is.
Goodstein’s theorem is a theorem about finite numbers that can be proven using infinite ordinals, and can’t be proven using just Peano Arithmetic. I take it that’s the kind of thing you’re asking about? Though I couldn’t tell you how useful that in turn is.