同质结构的多态性克隆（通用同质多态性和自动同源性）
Polymorphism clones of homogeneous structures (Universal homogeneous polymorphisms and automatic homeomorphicity)
摘要：
每一个函数的克隆都自然地配备了一个拓扑-逐点收敛的点式收敛拓扑。如果$\mathfrak{C}$与$\mathcal{C}$的成员的每个克隆同构已经是同胚（关于逐点收敛点式收敛拓扑），则称克隆$\mathfrak{C}$相对于克隆类$\mathcal{C}$具有自动同胚性。本文研究可数同构关系结构的多态克隆的自动同胚性质。为此，我们引入并利用普遍的同质多态性。接下来给出了自由齐次结构的多态克隆的自动同胚的两个类属准则，证明了具有自反序的类属偏序集的多态克隆具有自动同胚，具有严格序的类属偏序集的多态克隆具有关于可数$ω$ -范畴结构的自动同胚.我们的结果推广了Bodirsky，Pinsker和Pongrácz的结果.
英文摘要：
Every clone of functions comes naturally equipped with a topology---the topology of pointwise convergence. A clone $\mathfrak{C}$ is said to have automatic homeomorphicity with respect to a class $\mathcal{C}$ of clones, if every clone-isomorphism of $\mathfrak{C}$ to a member of $\mathcal{C}$ is already a homeomorphism (with respect to the topology of pointwise convergence). In this paper we study automatic homeomorphicity-properties for polymorphism clones of countable homogeneous relational structures. To this end we introduce and utilize universal homogeneous polymorphisms. Next to two generic criteria for the automatic homeomorphicity of the polymorphism clones of free homogeneous structures we show that the polymorphism clone of the generic poset with reflexive ordering has automatic homeomorphicity and that the polymorphism clone of the generic poset with strict ordering has automatic homeomorphicity with respect to countable $ω$-categorical structures. Our results extend and generalize previous results by Bodirsky, Pinsker, and Pongrácz.
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