Per Lindström’s work on interpretations has great beauty. He was a grand master of dazzling diagonal arguments. In this talk we will explain the basic setting underlying Per’s work. We introduce the notion of interpretation and provide some examples of interpretations. We show how, in the context of arithmetic, the notion of interpretability has an almost unrecognizable equivalent. This equivalence is known as the Orey–Hájek Characterization.

We will discuss some results of Per and have a look at further developments.