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.

单词	Prewellordering
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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