Last Updated：2025/11/23

(set theory, order theory) A total order of some set such that every nonempty subset contains a least element.

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well-order

Source Word

well-order

Noun

(set theory, order theory) A total order of some set such that every nonempty subset contains a least element.

Japanese Meaning

（集合論、順序理論において）任意の非空部分集合に最小元を持つ全順序（全順序関係）のこと。

The mathematician showed that every countable ordinal admits a well-order, which made transfinite induction straightforward.

その数学者は、すべての可算順序数が各非空部分集合に最小元を持つ全順序を与えられることを示し、それによって超限帰納法が容易になった。

Sense（1）

(set theory, order theory) A total order of some set such that every nonempty subset contains a least element.

underline X is well-order enriched iff every morphism set underline X(X,Y) carries a well-order ≤_(XY) such that

f lneqq _(XY)g⇒h•f lneqq _(XY)h•g

for every h:Y→Z.

well-orders

（ plural ）