Title: Comparing Computational Power
Abstract: It is standard to assert that a computational model (set of partial functions) M is as powerful as a model M' by fixing a 1-1 mapping between their domains and showing that every function of M' is simulated by some function of M. We show that in the general case a model can be of equivalent power to a proper superset of itself. Define a model that is strictly weaker than all its supersets as 'robust'. We describe several results regarding robustness. In particular, the set of recursive functions is robust. Accordingly, we provide a criterion for verifying that a model, operating over an enumerable domain, is super-recursive.