Submission date: 2 September 2021

Abstract:

'Skolem arithmetic' is the complete theory T of the multiplicative monoid (ℕ, ·). We give a full characterization of the &empy;-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.

Mathematics Subject Classification:

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Full text arXiv 2109.01131: pdf, ps.