Abstract‘Skolem arithmetic’ is the complete theory T of the multiplicative monoid. We give a full characterization of the ‐definable stably embedded sets of T, showing in particular that, up to the relation of having the same definable closure, there is only one non‐trivial one: the set of squarefree elements. We then prove that T has weak elimination of imaginaries but not elimination of finite imaginaries.

Abstraction principles provide implicit definitions of mathematical objects. In this paper, an abstraction principle defining categories is proposed. It is unsatisfiable and inconsistent in the expected ways. Two restricted versions of the principle which are consistent are presented.