Oracle game semantics for the nu-calculus

The long-standing problem of giving fully abstract semantics to the nu-calculus have been solved only recently with game models à la Hyland-Ong in the universe of Fraenkel-Mostowski sets. However, these models are still quite complicated, mainly because they aim to ensure at once both the equivariance of strategies, and the possibility of having strategies generating new names. In this paper, we present an alternative, and somehow simpler, game semantics for the nu-calculus, endorsing the “object-oriented” view of references. The idea is to deal first with equivariance, and then with name generation. More precisely, we define a game model where terms are interpreted by (equivariant) strategies parametrized by some oracle, which can be seen as an “external supplier” of fresh names to be interrogated on the need. The oracle is provided at a second stage, when a model of complete strategies is defined by means of an extensional equivalence.