  We show how the language of Krivine's classical realizability may be used to
specify various forms of nondeterminism and relate them with properties of
realizability models. More specifically, we introduce an abstract notion of
multi-evaluation relation which allows us to finely describe various
nondeterministic behaviours. This defines a hierarchy of computational models,
ordered by their degree of nondeterminism, similar to Sazonov's degrees of
parallelism. What we show is a duality between the structure of the
characteristic Boolean algebra of a realizability model and the degree of
nondeterminism in its underlying computational model. ACM Reference Format:
Guillaume Geoffroy. 2018. Classical realizability as a classifier for
nondeter-minism.
