Ohio State University

**Abstract:**

The notion of $\Sigma_n$-elementary substructure over simple
languages on the ordinals allows for powerful applications in proof
theory and

leads to a general approach in the theory of ordinal numbers.

I will illustrate this by sketching the consistency of Reinhardt's
Strong Mechanistic Thesis with Epistemic Arithmetic (due to T.
Carlson), then briefly

showing how independence results can be obtained, and finally
giving some heuristics for ordinal notation systems which arise in a
new type of proof theoretic analyses.

SST 777

3 pm

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