quandles和field的不变普适性
Invariant universality for quandles and fields
摘要：
我们证明了可数quandles的可嵌入性关系和可数域的任何给定的特征以外的2是最大复杂的在一个强的意义上：他们是不变的普遍。这个概念来自于波莱尔约化理论，它指出标准波莱尔空间上的任何解析拟序本质上表现为同构不变博雷尔集的可嵌入关系的限制。作为一个中间步骤，我们证明了可数quandles的嵌入关系是一个完全的解析拟序。
英文摘要：
We show that the embeddability relations for countable quandles and for countable fields of any given characteristic other than 2 are maximally complex in a strong sense: they are invariantly universal. This notion from the theory of Borel reducibility states that any analytic quasi-order on a standard Borel space essentially appears as the restriction of the embeddability relation to an isomorphism-invariant Borel set. As an intermediate step we show that the embeddability relation of countable quandles is a complete analytic quasi-order.
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