Finality regained: A co-algebraic study of Scott-sets and Multisets

Abstract

In this paper we study iterated circular multisets in a coalgebraic frame- work. We will produce two essentially different universes of such sets. The unisets of the first universe will be shown to be precisely the sets of the Scott universe. The unisets of the second universe will be precisely the sets of the AFA-universe. We will have a closer look into the connection of the iterated circular multisets and arbitrary trees.