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Well partial order

In mathematics, a well partial order is a partial order ≤ with the property that, for any infinite sequence x1, x2, x3..., there must exist distinct indices i and j with xi ≤ xj.

Stated less formally, a well partial order has no infinite sequences that have no duplicate elements and never go up. This is a generalization to partial orders of well orders, which are total orders that have no infinite sequences that always go down. For total orders these two statements are equivalent, meaning that any well order is also a well partial order, but for partial orders it may be that at many steps the sequence goes neither up nor down.

Table of contents
1 Examples
2 History
3 Applications

Examples

History

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Applications

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