We study punctual categoricity on a cone and intrinsically punctual functions and obtain complete structural characterizations in terms of model-theoretic notions. As a corollary, we answer a question of Bazhenov, Downey, Kalimullin, and Melnikov by showing that relational structures are not punctually universal. We will also apply this characterisation to derive an algebraic characterisation of relatively punctually categorical mono-unary structures.

中文翻译：

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准时在结构上的可定义性

我们研究锥体上的守时分类和本质上的守时功能，并根据模型理论概念获得完整的结构特征。作为推论，我们通过证明关系结构不是守时的普遍性来回答巴真诺夫，唐尼，卡利姆林和梅尔尼科夫的问题。我们还将应用此刻画推导相对准时分类的一元结构的代数刻画。