When talking to a friend recently he asked a question - are there any reasonable first-order theories which have proof theoretic ordinal equal to small or large Veblen ordinal? I have then extended his question broadly - which ordinals can be proof-theoretic ordinals of any "reasonable" theory, where by "reasonable" I suggested we should mean "extending PA", though this can be discussed.

Another, related question is the following: what is the proof-theoretic ordinal of theory PA+"$\varepsilon_0$ is well-founded"? I think it might be $\varepsilon_1$, but I can't be sure.

Thanks in advance for feedback!