Identifiability guarantees that the mathematical model of a dynamic system is well-defined in the sense that it maps unam-biguously its parameters to the output trajectories. This paper casts identifiability in a set-membership (SM) framework and relates recently introduced properties, namely SM-identifiability, µ-SM-identifiability, and ε-SM-identifiability, to the properties of parameter estimation problems. Soundness and ε-consistency are proposed to characterize these problems and the solution returned by the algorithm used to solve them. This paper also contributes by carefully motivating and comparing SM-identifiability, µ-SM-identifiability and ε-SM-identifiability to related properties found in the literature and by providing a method based on Differential Algebra to check these properties.