(Liverpool)

We will discuss the nature of the extensional ordering on structure Q_\sigmaof the hereditarily sequential functionals of finite types.

It was shown by Dag Normann that it is non-dcpo.

On the other hand, it still has good domain theoretical properties if to generalise Scott domains

to so called natural domains.

From the traditional domain theoretic point of view, it is not only non-dcpo, but the posets

of sequential functionals and finite sequential functionals have anomalies which we

(in a joint work with Dag Normann) characterised with a focus on:

* when the sequential functionals of a given type form a directed complete partial ordering (dcpo),

* and when a finite sequential functional will be the nontrivial least upper bound of an infinite chain

of sequential functionals.

Robert Recorde Room

Department of Computer Science