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词汇 Prewellordering
分类 英语词汇 英语翻译词典
释义

Prewellordering

英语百科

Prewellordering

In set theory, a prewellordering is a binary relation \le that is transitive, total, and wellfounded (more precisely, the relation x\le y\land y\nleq x is wellfounded). In other words, if \leq is a prewellordering on a set X, and if we define \sim by

then \sim is an equivalence relation on X, and \leq induces a wellordering on the quotient X/\sim. The order-type of this induced wellordering is an ordinal, referred to as the length of the prewellordering.

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