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Ordinal analysis is typically described as characterizing recursive ordinals in a theory $T$, but there is a sense in which it can characterize all $T$-ordinals, even those that are nonrecursive. ...

In Ordinal Analysis, Proof-theoretic Ordinal of a theory is thought as measure of a consistency strength and computational power. Is it always the case? I. e. are there some general results about ...

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 ...