Standardness via non-standardness

Jaime Gaspar

In this talk we present the following theorem: non-standard arithmetic with some principles is conservative over standard arithmetic. We start by introducing two notions: (1) standard arithmetic; (2) non-standard arithmetic with principles.
Then we sketch the proof of the theorem in three steps: (1) we introduce a tool called Shoenfield-like bounded functional interpretation of non-standard arithmetic; (2) we introduce another tool called flattening; (3) we apply the two tools.

We keep this talk very short, simple and sweet.