Abstract

hereditarily-sequential functionals is not ω-complete (in contrast to the old fully abstract continuous dcpo model of Milner). This is also applicable to a potentially (universal) model for PCF + = PCF + pif (parallel if). 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 (with respect to existing directed ‘pointwise’, or ‘natural ’ least upper bounds). 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. Key words: domain theory, dcpo and non-dcpo domains, Scott topology,

Citations