Well-quasi-ordering

In mathematics, specifically order theory, a well-quasi-ordering or wqo is a quasi-ordering such that any infinite sequence of elements ${\displaystyle x_{0}}$, ${\displaystyle x_{1}}$, ${\displaystyle x_{2}}$, … from ${\displaystyle X}$ contains an increasing pair ${\displaystyle x_{i}\leq x_{j}}$ with ${\displaystyle i<j}$.

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Wikipedia