On universal algebra over nominal sets

Nominal sets were introduced by Gabbay and Pitts (Gabbay and Pitts, 1999). This paper describes a step towards universal algebra over nominal sets. There has been some work in this direction, most notably by M.J. Gabbay (Gabbay, 2008). The originality of our approach is that we do not start from the analogy between sets and nominal sets. As shown in (Gabbay, 2008), this is possible, but it requires ingenuity and ad hoc constructions. For example, the logic of (Gabbay, 2008) is not standard equational logic and even fundamental notions such as variables and free algebras have to be revisited.