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Some model theory of $\operatorname{Th}(\mathbb{N},\cdot)$ by Stonestrom, Atticus is a scholarly article available to read on EtoBox.

What is Some model theory of $\operatorname{Th}(\mathbb{N},\cdot)$ about?

'Skolem arithmetic' is the complete theory $T$ of the multiplicative monoid $(\mathbb{N},\cdot)$. We give a full characterization of the $\varnothing$-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.

Author

Stonestrom, Atticus

Published

2021

Language

EN