  Orbit-finite sets are a generalisation of finite sets, and as such support
many operations allowed for finite sets, such as pairing, quotienting, or
taking subsets. However, they do not support function spaces, i.e. if X and Y
are orbit-finite sets, then the space of finitely supported functions from X to
Y is not orbit-finite. In this paper we propose two solutions to this problem:
one is obtained by generalising the notion of orbit-finite set, and the other
one is obtained by restricting it. In both cases, function spaces and the
original closure properties are retained. Curiously, both solutions are
"linear": the generalisation is based on linear algebra, while the restriction
is based on linear logic.
