Since many of the main tools in model theory, for example the switching to an elementary extension, do not work for finite structures, one can take a particular interest in pseudo-finite structures, which are infinite structures that behave sufficiently similar to finite ones. One also might be interested in an overview of the definable sets in a given pseudo-finite structure up to isomorphism. For this goal invariants of definable sets are a useful tool, especially one can define a stronger, non-standard version of cardinality for definable sets that is invariant under definable bijections. We will break this invariant down into components which are easier to understand and review their relations. We will also ask ourselves, how conclusively this version of cardinality describes the definable sets in certain types of pseudo-finite structures.