On the extensional ordering of the sequential functionals

Vladimir Sazonov

(Liverpool)

We will discuss the nature of the extensional ordering on structure Q_\sigma
of 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.

Tuesday 26th October 2010, 14:00
Robert Recorde Room
Department of Computer Science