Abstract
The question of the decidability of the observational ordering of finitary PCF was raised (Jung and Stoughton, in: M. Bezem, J.F. Groote (Eds.), Typed Lambda Calculi and Applications, Lecture Notes in Computer Science, vol. 664, Springer, Berlin, 1993, pp. 230–244) to give mathematical content to the full abstraction problem for PCF (Milner, Theoret. Comput. Sci. 4 (1977) 1–22). We show that the ordering is in fact undecidable. This result places limits on how explicit a representation of the fully abstract model can be. It also gives a slight strengthening of the author's earlier result on typed λ-definability (Loader, in: A. Anderson, M. Zeleny (Eds.), Church Memorial Volume, Kluwer Academic Press, Dordrecht, to appear).
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