 The full abstraction problem for PCF consists in finding a direct description of the class of domains and continuous functions that make up the fully abstract model. A solution to this problem would require a precise criterion for assessing the extent to which a proposed description of the model is satisfactory. If one accepts the “precise minimal condition that a semantic solution of the full abstraction problem should satisfy” given by Jung &amp; Stoughton (1993), namely the possibility of describing in an effective way the domains \(D^\sigma\) of a finitary version of PCF (whose only ground type is bool), then the story of failed attempts to give such a direct description of the fully abstract model is justified, with hindsight, by a result of Loader (2001):