Abstract

As Dag Normann has recently shown, the fully abstract model for PCF of hereditarily-sequential functionals is not ω-complete . This is also applicable to a potentially wider class of models such as the recently constructed by the author fully abstract model for PCF+=PCF+pif . Here we will present an outline of a general approach to this kind of ‘natural’ domains which, although being non-dcpos, allow considering ‘naturally’ continuous functions . There is also an appropriate version of ‘naturally’ algebraic and ‘naturally’ bounded complete ‘natural’ domains which serves as the non-dcpo analogue of the well-known concept of Scott domains, or equivalently, the complete f-spaces of Ershov. It is shown that this special version of ‘natural’ domains, if considered under ‘natural’ Scott topology, exactly corresponds to the class of f-spaces, not necessarily complete