The ANTI-order and the fixed point property for caccc posets Original Research Article

This paper settles a conjecture made in (Li [2]) that, if 〈Pξ: ξ ⩽ λ〉 is an ANTI-perfect sequence in a connected caccc poset having no one-way infinite fence, then either there are ξ < λ and x ∈ Pξ ∈ Pξ+1 such that Pξ(> x) and Pξ(< x) are both fixed point free (fpf), in which case P is also fpf, or P has the fixed point property (fpp) if and only if Pλ has the fpp.