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Deviation of a poset

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In mathematics, the deviation of a poset is an ordinal number measuring the complexity of the poset.

Definition

A poset is said to have deviation at most α (for an ordinal α) if for every descending chain of elements a0 > a1 >...all but a finite number of the posets of elements between an and an+1 have deviation less than α.

Not every poset has a deviation: a necessary and sufficient condition for a poset to have a deviation is that it does not contain a subset isomorphic to the rational numbers.

References

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