A long series of conversations interweaving mathematical, historical and philosophical aspects of categoricity in model theory took place between the author and Saharon Shelah in 2016 and 2017. In this excerpt of that long conversation, we explore the relationship between explicit and implicit aspects of categoricity. We also discuss the connection with definability issues.

中文翻译：

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分类、外部和内部：摘自与 Saharon Shelah 的对话

作者与 Saharon Shelah 于 2016 年和 2017 年进行了一系列将模型理论中范畴性的数学、历史和哲学方面交织在一起的长对话。在这段漫长对话的摘录中，我们探讨了范畴性的显性和隐性方面之间的关系。我们还讨论了与可定义性问题的联系。