Some model theory of Th(N,·)$\operatorname{Th}(\mathbb {N},\cdot )$

Mathematical Logic Quarterly 68 (3):288-303 (2022)
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Abstract

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.

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10.1002/malq.202100049

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Quasi-o-minimal structures.Oleg Belegradek, Ya'acov Peterzil & Frank Wagner - 2000 - Journal of Symbolic Logic 65 (3):1115-1132.
How Big Should the Monster Model Be? [REVIEW]John T. Baldwin - 2015 - In Åsa Hirvonen, Juha Kontinen, Roman Kossak & Andrés Villaveces (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics. Boston: De Gruyter. pp. 31-50.

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