Guillaume Geoffroy (Institut de Mathématiques de Marseille), Connecting degrees of parallelism and Boolean algebras through classical realizability



Non-fully abstract models of PCF and related systems typically contain so-called non-sequential functions : for example, Scott's model of continuous functions has parallel or, while Berry's stable functions have Gustave's function. Using constructs which come from Krivine's classical relizability (notably the characteristic Boolean algebra Gimel 2), we show how these non-sequential functions and the question of their relative strength (in terms of their ability to emulate one-another) can be connected to the theory of Boolean algebras.