Abstract

The main result of this paper provides a necessary and sufficient condition that the function space [ D → D] of a domain (ω-algebraic cpo) D be again a domain. The condition— confirming a conjecture of Plotkin—is that D be strongly algebraic (≡SFP). The importance of this is that it enables us to conclude that SFP is the largest category of domains that is closed under the constructions of interest in semantics. In the final section we briefly consider how our results may need to be extended if our, admittedly rather restrictive, notion of ‘category of domains’ is relaxed in certain ways.

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