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The strong order property 1 (SOP \(_{1}\) ) is a model-theoretic tree property introduced by Džamonja and Shelah. We give an exposition of a family of results around NSOP \(_{1}\) theories, explaining why the NSOP \(_{1}\) /SOP \(_{1}\) divide is a meaningful dividing line among first-order theories. This involves summarizing work on Kim-independence and on the interpretability order, as well as aspects of Mutchnik’s work on SOP \(_{1}\) and SOP \(_{2}\) .

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NSOP1 as a Dividing Line

  • 会议论文

  • 发表日期：

    2025年

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  • Nicholas Ramsey

摘要

The strong order property 1 (SOP \(_{1}\) ) is a model-theoretic tree property introduced by Džamonja and Shelah. We give an exposition of a family of results around NSOP \(_{1}\) theories, explaining why the NSOP \(_{1}\) /SOP \(_{1}\) divide is a meaningful dividing line among first-order theories. This involves summarizing work on Kim-independence and on the interpretability order, as well as aspects of Mutchnik’s work on SOP \(_{1}\) and SOP \(_{2}\) .