构造任意集合上刚性二元关系定理的一个强形式
A stronger form of the theorem constructing a rigid binary relation on any set
摘要：
在每一个集合A上都有一个严格的二元关系，即这样一个关系R \subseteq A \times A，除了恒等式之外，没有同态（A，R）\rightarrow（A，R）（Vop{gyrinidae}nka et al. [1965]）。证明了对任意无穷基数κ，若卡A \leq 2^κ，则存在关系R \subseteq A \times A具有如下性质：\forall（x \in A）\exists（{x} \subseteq A（x）\subseteq A，卡A（x）\leq κ）\forall（f：A（x）\rightarrow A，f \neq id_A（x））f不是R的同态.上述性质意味着R是刚性的。如果关系R \subseteq A \times A具有上述性质，则卡片A \leq 2^κ。
英文摘要：
On every set A there is a rigid binary relation i.e. such a relation R \subseteq A \times A that there is no homomorphism (A,R) \rightarrow (A,R) except the identity (Vop{ě}nka et al. [1965]). We prove that for each infinite cardinal number κif card A \leq 2^κ, then there exists a relation R \subseteq A \times A with the following property: \forall (x \in A) \exists ({x} \subseteq A(x) \subseteq A, card A(x) \leq κ) \forall (f: A(x) \rightarrow A, f \neq id_A(x)) f is not a homomorphism of R. The above property implies that R is rigid. If a relation R \subseteq A \times A has the above property, then card A \leq 2^κ.
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