## 6.5Principal Order Ideals and Farey Subsequences

In this section we define Farey subsequences which can be useful for the existence problems on the relatively blocking elements in posets.

Let {a} be a nontrivial one-element antichain of a finite bounded poset P. Consider the sequence of irreducible fractions

arranged in increasing order. Note that (P, a; ω) is a subsequence of the Farey sequence of order ω(P).

We always ...

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