Abstract
Nominal sets, introduced to Computer Science by Gabbay and Pitts, are useful for modeling computation on data structures built of atoms that can only be compared for equality. In certain contexts it is useful to consider atoms equipped with some nontrivial structure that can be tested in computation. Here, we study nominal sets over atoms equipped with both relational and algebraic structure. Our main result is a representation theorem for orbit-finite nominal sets over such atoms, a generalization of a previously known result for atoms equipped with relational structure only.
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