A note on prime models in weakly o‐minimal structures

Mathematical Logic Quarterly 63 (1-2):109-113 (2017)
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Abstract

Let be a weakly o‐minimal structure with the strong cell decomposition property. In this note, we show that the canonical o‐minimal extension of is the unique prime model of the full first order theory of over any set. We also show that if two weakly o‐minimal structures with the strong cell decomposition property are isomorphic then, their canonical o‐minimal extensions are isomorphic too. Finally, we show the uniqueness of the prime models in a complete weakly o‐minimal theory with prime models.

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Citations of this work

Strong cell decomposition property in o-minimal traces.Somayyeh Tari - 2020 - Archive for Mathematical Logic 60 (1):135-144.

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References found in this work

Weakly o-minimal nonvaluational structures.Roman Wencel - 2008 - Annals of Pure and Applied Logic 154 (3):139-162.
Elimination of quantifiers for ordered valuation rings.M. A. Dickmann - 1987 - Journal of Symbolic Logic 52 (1):116-128.

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