We prove that weakly o-minimal theories of finite convexity rank having less than 2 countable models are binary. Our main result is the confirmation of Vaught’s conjecture for weakly o-minimal theories of finite convexity rank.

中文翻译：

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有限凸秩的弱 o-极小理论的 Vaughts 猜想

我们证明了具有少于 2 个可数模型的有限凸性秩的弱 o-极小理论是二元的。我们的主要结果是对有限凸秩的弱 o-极小理论的 Vaught 猜想的证实。