Juan Aguilera

The Pi^1_2 Consequences of a theory

We define the \Pi^1_2-norm |T| of a theory T, an analogue of the proof-theoretic ordinal of T for statements of complexity \Pi^1_2. We go over the basic theory of |T| and use it to define the \Pi^1_2-soundness ordinal of T. Then, we characterise the recursive and admissible ordinals which are \Pi^1_2-soundness ordinals of some recursively enumerable extension of Arithmetical Comprehension. This is joint work with Fedor Pakhomov.