论文标题
连续逻辑中的大致分类
Approximate Categoricity in Continuous Logic
论文作者
论文摘要
我们探索了本文中引入的失真系统背景下的近似分类，这是Ben Yaacov引入的扰动系统的轻度概括。我们将Ben Yaacov的Ryll-Nardzewski样式将大约分类理论从扰动系统的上下文扩展到失真系统的上下文。我们还朝着对莫利定理的类似物的类似物而取得了进展，以使其不可分割的近似分类性，这表明，如果有一些不可数的基本$κ$，以至于每个大小$κ$的每个模型都属于“近似饱和”，那么所有不可衡量的红心都相同。最后，我们介绍了这些现象的一些例子，并强调了普通可分离分类性与不可分割的近似类别之间的明显相互作用。
We explore approximate categoricity in the context of distortion systems, introduced in our previous paper, which are a mild generalization of perturbation systems, introduced by Ben Yaacov. We extend Ben Yaacov's Ryll-Nardzewski style characterization of separably approximately categorical theories from the context of perturbation systems to that of distortion systems. We also make progress towards an analog of Morley's theorem for inseparable approximate categoricity, showing that if there is some uncountable cardinal $κ$ such that every model of size $κ$ is 'approximately saturated,' in the appropriate sense, then the same is true for all uncountable cardinalities. Finally we present some examples of these phenomena and highlight an apparent interaction between ordinary separable categoricity and inseparable approximate categoricity.
