An Alternative Order for the Failures Model

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Abstract
The failures-divergences model for CSP is usually presented with the refinement order being the one used for fixed points in the semantics of recursion. The requirement that this order be complete means that the model needs a compactness axiom closely related to an assumption of finite non-determinism. We show that a second and stronger order exists which does not need compactness to make it complete, but which gives exactly the same least fixed points as the refinement order. The new order allows us to prove some new results about the semantics, and to justify versions of recursion induction. In pursuit of this last topic we develop various topologies over the model.

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