### The Pi^1_2 Consequences of a theory

Logic and Set Theory Seminar

15th December 2021, 4:30 pm – 6:00 pm

Zoom, https://bristol-ac-uk.zoom.us/j/9513231678?pwd=cjgvTjR3VEdiTTFzdWdvdFNTTU9FZz09

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.

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