# Computability on Abstract Objects

## Ulrich Berger

(University of Wales Swansea)

Three different notions of computability for functions on abstract objects like e.g. the real numbers are discussed: 1. effective operations, i.e. functions which can be traced by a recursive mapping on the codes of their inputs and outputs, 2. effectively continuous functions, i.e. functions induced by a recursive mapping on finite approximations of their inputs, 3. functions definable from certain basic functions by certain operations like composition, recursion etc. It turns out that in many interesting cases these three notions coincide, i.e. characterise the same class of functions. We also consider situations where coincidence does not hold or is still open.

**Tuesday 9th November 1999, 15:00**

Seminar Room 322

Department of Computer Science