The sequentially realizable functionals

In the previous chapter, we saw how the model PC offers a ‘maximal’ class of partial computable functionals strictly extending SF (in the sense of the poset \(\mathcal{J}(\mathbb{N}_\bot)\) of Subsection 3.6.4). In the present chapter, we show that SF can also be extended in a very different direction to yield another class SR of ‘computable’ functionals which is in some sense incompatible with PC. This class was first identified by Bucciarelli and Ehrhard [45] as the class of strongly stable functionals; later work by Ehrhard [69], van Oosten [294] and Longley [176] established the computational significance of these functionals, investigated their theory in some detail, and provided a range of alternative characterizations.

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