# Notations for Iterations (Panzerdivision proof theory done properly)

## Harold Simmons

(Manchester University)

Some of you may have seen some of the topic of `ordinal notations' and been impressed, or perhaps not. The standard approach to this topics obscures a lot of what is going on, and often misses the point. In fact, it is about the nesting of iterations and how complicated thees can become.

In this talk I will explain some of the background from the stand point of iterations. I will then go on to describe an applied lambda-calculus with explication notations for these gadgets. Finally, I will indicate how these notations are related to the standard Bachmann notations.

The first part of the talk should be understandable without a knowledge of ordinals.

**Wednesday 7th May 2003, 14:00**

Robert Recorde Room

Department of Computer Science